Lighting – Will a feed through on and off switch work with a fluorescent light

You shouldn't have any issue. Alot of ballasts are rated 120v/240v. A regular wall outlet is usually 15a 120v. Which you should be fine. Is this a t8 t5 or t12 fluorescent light fixture. I mean it is possible that you have a bad ballast that is only providing the proper power to the socket for only the bulb that lit. Try taking the bulb that is lit out of that side and switch it to the side that isn't lit. That should give you a rough idea that something is wrong. Check the connections at the socket of the side that isn't lit make sure the wires are actually in the socket. But again test the other side with the good bulb. sounds like a bad ballast in my opinion. But again no...plugging it in shouldn't have hurt anything. Getting power that way isn't really any different than hard wiring it.

The basic problem is that the occupancy switch that you chose to purchase is one designed to be able to work in series with the load attached to it. If the attached load is too small (too low of wattage) the switch assembly does not get enough power to operate correctly. For the particular model you have this is on the order of 40 to 50 watts of minimum load. From a technical standpoint it kind of sucks that they work this way BUT they are designed to work in place of a simple light switch that is in in series with its load.

Your Radio Shack relay does not come close to representing a 40-50W load on the switch so the only other way is to add some additional load in series with the switch (i.e. equivalently in parallel with the relay coil). As you have come to see this is not a very satisfactory solution and some other scheme needs to be found.

The best situation in this case is to acquire the alternate type of occupancy switch as mentioned in that thread that you linked. That type of switch has a live AC lead and neutral AC lead connected to it to power the switch unit irrespective of the size of the load. A separate output connection goes off to the load you are trying to switch. This type of switch may take a little re-wiring in your garage but that should be easier than trying to wire in the kludged extra load that the current switch requires. If you choose to deploy this improved version of the switch you will be able to remove the Radio Shack relay from the installation.

To make yourself feel better about the fact that you now have an extra occupancy switch you could pick a room in your house that has a tendency to get its light left on accidentally and install the extra unit in place of its light switch. Maybe this is a bathroom the kids use or a far closet that does not get used often.

BTW

It looks like Leviton now has a whole slew of different model occupancy switches that are also designed for single pole switch replacement but have removed the minimum load requirements. These do not require a neutral wire connection but do require a GND wire connection.