The starter solenoid takes a good few amps to throw, especially when they're old and tired. It's also a big electromagnet (inductor) so current lags behind voltage, which can cause the ignition switch to arc.
While the bulkhead relay (not solenoid, since its only function is to actuate another set of electrical contacts) is not original, its not a bad upgrade in a system which is known to have a weak ignition switch.
While some of the wiring needs tidying up, it looks like some effort has been made.
I'd recommend printing out the toyota diagram as a starting point, and then editing it to bring into line with what you have.
You'll probably find that it's not actually that much different, and then decide what to do.
FWIW, my money is on a corroded ignition switch connector wire/terminal