I think you are on the right track. Mine was operating on 12 volts. It worked well until it managed to operate on its own and blared until it was shut down ..about 5 minutes!
When I opened the unit the wire joints were all desoldered (probably due to excessive heat). But the relay coil and contacts still seem ok. And I think the heat affected the old wire-wound resistor.

I would like to replace it with an equivalent ..if I know its values (ohms and watts).

Any spec info on this is appreciated.