I can close off this thread now. I bought the $200 relay and installed it. Everything is now working properly. I took the old one apart. It is a simple solenoid. It isn't electronic and its not a relay. It has two terminals with #awg 20 or so wires that excite the solenoid, moving a heavy metal lump to compress a spring and bring another heavy lump of copper against the two big terminals that have #00 or so, wires attached and that close a circuit between the two sets of batteries. Those terminals and the second metal lump are covered in green and black corrosion, so not making good, if any contact. those corroded terminals are within the end cap of the solenoid, protected from moisture by gaskets. Ha! All the gaskets seem to do is to make sure any moisture that enters can never leave, thus encouraging a quick death when the moisture enters. ( We are is the desert! It is very dry here. I haven't seen moisture anywhere, yet this solenoid has enough inside that end cap to kill it!). We are returning to BC next week, where it rains a lot. hopefully the new solenoid will be happier in the rain than it has been in the desert.