Re: Could this connection cause damage?
Your problem is unlikely to be directly related to engine heat and I don't think the EA EEC-IV is smart enough to turn off the fuel pump on an over heating engine.
When you turn the key to "run" (not start), normally your ECU will turn on the fuel pump for about 4 seconds and will then turn it off if it does not see any ignition pusles. You can normally hear this from outside the car. Listen near the fuel tank (might need two people). It does this via the fuel pump relay. You should also be able hear the relay click as the ECU turns the pump on and off.
If you're not sure which relay it is, check the wire color on the relay and the fuel pump (make sure you look at the color on the main loom plug to the pump, as the wires directly connected to the pump may be different).
If you test this when cold and test it again when hot, you should be able to figure out if the problem comes from the relay or the fuel pump.
I would be surprised if there were any electronic components in the fuel pump relay. Normally they are just an electromagnetic switch. I don't have an EA manual handy, but in the XF EFI you can use any old relay for the fuel pump and I'd be 99% sure you can with an EA too.
EFI pumps are susceptable to dirt and can seize up quite easily. I had an ED that stopped due to small pieces of grit in the pump. I replaced the pump, but was able to shake the grit out of the old one and get it going again. It's now a spare. Fuel additives will not help if you have a grit problem.
You could put a push button switch on the fuel pump, but make sure it's a push button (not permanently on). You don't want high pressure fuel gushing from a split fuel line if you have an accident. (Normally the ECU will turn the pump off 4 seconds after the engine stops, see above)