Does sound like the solenoid on the starter to me, quite a common issue on older starters. I have a link in my signature block on overhauling the starter/solenoid (although the tutorial is for a gs300, they are all the same design). As Colin mentions, worth checking the relay 1st, and the starter is in the V. If you are handy with a socket set and spanners, it is actually quite an easy job getting the inlet manifold off, albeit a bit fiddly. I had to take mine off to replace one of the knock sensors recently. Coolant doesn't need a complete drain down, just pop the thermostat housing off and that is enough. The inlet manifold to block gaskets are not reusable, neither is the throttle body gasket, so you may want to tee those up before hand if you don't want to gamble on reusing them.
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