[SalesForce] trigger.OldMap != trigger.newMap test class. Cannot cover update condition

I have a trigger that has two conditions, insert and update. On my update condition, I check to see if the Billing Zip Code has changed, if it has, the trigger fires.

My trigger works fine but I cannot cover the update condition with my test class for some reason. I can cover the update line but nothing after. It looks like the test class isn't getting the trigger to fire when I update the Billing Postal code in my test class.

Trigger:

trigger updateTerritoryonAccount on Account (before insert) {

    Map<String, String> map_ZipCode_TerrID = new Map<String, String>();
    Map<Id,Id> taMap = new Map<Id,Id>();
    for(Territory__c tr: [Select id,Zip_Codes__c, name from Territory__c where Zip_Codes__c != null AND Active__c != False]){
        for(String s : tr.Zip_Codes__c.split(',',0)){
            map_ZipCode_TerrID.put(s.trim(), tr.id);
        }
    }

    for(Territory_Assignment__c ta : [SELECT Id, User__c, Territory__c from Territory_Assignment__c WHERE Territory__c IN :map_ZipCode_TerrID.values()]){
        taMap.put(ta.User__c,ta.Territory__c);
    }

    if(Trigger.isInsert){
    for(Account a : Trigger.new){
        a.Territory__c = null;
        if(a.BillingPostalCode != null && a.BillingPostalCode !='' && a.BillingPostalCode.length() >= 5){
            String PostalCode = a.BillingPostalCode.subString(0,5);
            if(map_ZipCode_TerrID.get(PostalCode) != null && map_ZipCode_TerrID.get(PostalCode) == taMap.get(UserInfo.getUserId())){
        system.debug('--------------map_ZipCode_TerrID.get(PostalCode)---------------'+map_ZipCode_TerrID.get(PostalCode));
                a.Territory__c = map_ZipCode_TerrID.get(PostalCode); 
            }
            else{
                a.AddError('Territory error. Either you do not have access to this Territory or a Territory does not exist that contains the zip code for this Account. Please see your Administrator');
            }
        }
      }
    }

    if(Trigger.isUpdate ){
    for(Account a : Trigger.new){
        if(trigger.newMap.get(a.id).BillingPostalCode != trigger.oldMap.get(a.id).BillingPostalCode){
        a.Territory__c = null;
        if(a.BillingPostalCode != null && a.BillingPostalCode !='' && a.BillingPostalCode.length() >= 5){
            String PostalCode = a.BillingPostalCode.subString(0,5);
            if(map_ZipCode_TerrID.get(PostalCode) != null && map_ZipCode_TerrID.get(PostalCode) == taMap.get(UserInfo.getUserId())){
                a.Territory__c = map_ZipCode_TerrID.get(PostalCode); 
            }
            else{
                a.AddError('Territory error. Either you do not have access to this Territory or a Territory does not exist that contains the zip code for this Account. Please see your Administrator');
            }
          }
        }
      }
    }
}

Test class:

@isTest
    public class Test_updateTerritoryonAccount {

        private static testmethod void updateTerritoryonAccount_testMethod(){

            Profile p = [SELECT Id FROM Profile WHERE Name = 'System Administrator'];

            User u = new User();
            u.FirstName = 'Test';
            u.LastName  = 'User12';
            u.Email     = 'testsuser@tests.com';
            u.Username  = 'testsuser@tests.com';
            u.Alias     = 'test23';
            u.ProfileId = p.id;
            u.TimeZoneSidKey    = 'America/Denver';
            u.LocaleSidKey      = 'en_US';
            u.EmailEncodingKey  = 'UTF-8';
            u.LanguageLocaleKey = 'en_US';
            insert u;

            Territory__c tr = new Territory__c ();
            tr.name = 'Test Tr';
            tr.Zip_Codes__c = '12345,14567,78741';
            insert tr;

            Territory_Assignment__c ta = new Territory_Assignment__c();
            ta.User__c = u.id;
            ta.Territory__c = tr.id;
            insert ta;

            system.runAs(u){
            test.startTest();

                    Account a2 = new Account();
                    a2.Name = 'Test Company';
                    a2.BillingPostalCode = '12345';
                    a2.BillingState = 'Texas';
                    a2.BillingStateCode = 'TX';
                    insert a2;

            test.stopTest();
            }
            try{
                    Account a3 = new Account();
                    a3.Name = 'Test Company';
                    a3.BillingPostalCode = '12345';
                    a3.BillingState = 'Texas';
                    a3.BillingStateCode = 'TX';
                    insert a3;

            }
            catch(Exception e){

            }
        }

        private static testmethod void updateTerritoryonAccount_testMethod2(){

                Profile p = [SELECT Id FROM Profile WHERE Name = 'System Administrator'];

            User u = new User();
            u.FirstName = 'Test';
            u.LastName  = 'User12';
            u.Email     = 'testsuser@tests.com';
            u.Username  = 'testsuser@tests.com';
            u.Alias     = 'test23';
            u.ProfileId = p.id;
            u.TimeZoneSidKey    = 'America/Denver';
            u.LocaleSidKey      = 'en_US';
            u.EmailEncodingKey  = 'UTF-8';
            u.LanguageLocaleKey = 'en_US';
            insert u;

            Territory__c tr = new Territory__c ();
            tr.name = 'Test Tr';
            tr.Zip_Codes__c = '12345,14567,78741';
            insert tr;

            Territory_Assignment__c ta = new Territory_Assignment__c();
            ta.User__c = u.id;
            ta.Territory__c = tr.id;
            insert ta;

            Account a = new Account();
            a.Name = 'Testing ACcount1';
            insert a;

            system.runAs(u){
                a.BillingPostalCode = '12345';
                update a;
            }
        }
    }

Part of test class that isn't covered in update condition:

for(Account a : Trigger.new){
        if(trigger.newMap.get(a.id).BillingPostalCode != trigger.oldMap.get(a.id).BillingPostalCode){
        a.Territory__c = null;
        if(a.BillingPostalCode != null && a.BillingPostalCode !='' && a.BillingPostalCode.length() >= 5){
            String PostalCode = a.BillingPostalCode.subString(0,5);
            if(map_ZipCode_TerrID.get(PostalCode) != null && map_ZipCode_TerrID.get(PostalCode) == taMap.get(UserInfo.getUserId())){
                a.Territory__c = map_ZipCode_TerrID.get(PostalCode); 
            }
            else{
                a.AddError('Territory error. Either you do not have access to this Territory or a Territory does not exist that contains the zip code for this Account. Please see your Administrator');
            }