In the FJ60 the starter solenoid is the relay. The circuit runs from a terminal on the ignition switch, to the starter solenoid, and a power feed from the battery with both grounding through the starter. The red line (I added for ease of eyes) is the wire that often degrades over time...its a...
Units like this are very common too as many older American cars used these.
The new heavier battery cable connects to the larger side posts (one to the battery, the other to the trigger terminal on the starter solenoid. One of the front posts is where you connect the OEM trigger wire that...
First time I experienced a starter click with a hot car was with my 1975 Saab 99 because the starter was located under the headers. I replaced the starter over and over again each one warranted and it solved the problem for a few months and always came back. In the end an old school Saab tech...
It is very common for the solenoid trigger wires to age and suffer a greater voltage drop. You can run new wires for this circuit or simply install a new fender mount relay with heavier wires to the solenoid and then use the current starter wires to trigger the new relay.