You have an arc-over somewhere in your power supply system. Electric arcs produce a broad band signal with precisely that noise pattern.
Cracked or dirty insulators on the power poles, transformer with an internal primary circuit fault, loose connections between the transformer and meter, or compromised underground feeder cables that are leaking current between the conductors will probably be the source of this EMI.
Heaven forbid that the source is anywhere in the house, that's a dangerous situation.
Determining where it comes from
Given the noise that can be heard in the video, this should be transmitting a pretty nasty interference on AM radio frequencies to the point you should have no problem using an AM radio as a source detector.
First steps are to make sure this isn't something in the house that is suffering from a loose connection, ground leakage or arc fault. Turn your radio on and with it somewhere mid band between stations, see if you can hear the noise. Now go through the breaker panel or fuse panel and cut power to each circuit till you have cut all power to the house.
If the noise goes completely away from powering off a circuit, then start looking for appliances, switches, lighting fixtures powered by that circuit that that have failures. At this point, if wiring starts being the possible culprit, you're getting into electrician territory, so get a qualified electrician if you're exceeding your technical expertise or what you're allowed to do under your local laws.
Using this method, I had found that the people who wired my house up had used a crimp ground ring to complete a power circuit in the bathroom which explained the radio noise and the dim lighting that would flicker every so often. Removing the electrician's tape off the odd looking connection revealed that the crimp ring (improper use, only supposed to be used in the ground circuit) had worked loose and the copper wire was being slowly eroded from the arcing in the loose connection.
If the power down only slowly diminishes the noise till the last circuit is cut off, then you need to make sure the power entrance and cabling to the breaker panel/fuse panel are intact to clear your residence (qualified electrician time, you do not want to be messing with this).
Once you have cleared your residential wiring, then you need to get the power company involved in hunting down where the noise is emanating from. It's in their best interest to fix it if its a bad splice, cracked insulator or transformer getting ready to blow.
Best Answer
The clicking noise sounds like a contactor or power relay. On the tubs I have worked on there has been a safety pressure switch on the pump, no pressure the switch opens and the heat contactor drops out. Other possible problems include a rusty contactor trying to pull in, loud buzz because it's not fully closing. I would check the pressure switch and look for a possible thermal overtemp switch also. Loose or corroded connections are quite possible also. So an inspection of the connections could also identify the problem. The contactor issue needs to be fixed but you can test the heater with the power off, measure the terminals with an ohm meter the value will probably be 10-30 ohms if it shows open it is bad. The resistance is based on the size of the heat element so it could be lower or higher but will probably be close to 10-30 ohms. I have bypassed both pressure switches and over temp switches to verify that is the problem but once solved never leave a safety bypassed.