it acts like the battery is dead after it's hot.
"Heat soak" resulting in high resistance in the starter/solenoid or dirt/oil in starter solenoid face/contact plate???......it's got an oil leak and it's 20 years old.....
Try putting a relay into the cicuit to the starter slenoid feed and a short run of heavy wire direct from battery to solenoid via this new relay.
Maybe best to confirm the present problem when hot by feeding battery power direct to solenoid using a temporary jumper/feed wire.
Also fix the oil leak!!1......oil leaks attract dirt which attracts problems......use aerosol Electrical Contact Cleaner or even Brake Cleaner spray to clean up the electricals.