Issue causing starter to stay engaged on warm starts
I just picked up this IS300 about a month ago. It's a 2001 year automatic and has 145k miles on it. The car seems to have had a hard life that includes some body damage that's been repaired with too much body filler and miss-matched bumpers, etc. Looks aside, I'm trying to keep this reliable for my wife, but it has one rather annoying issue.
This happens occasionally but not consistently and only when the vehicle has been at operating temp for some time. I am going to try to explain this as best I can.
Lets say I drive down to the store to grab some milk. I park the hot car and shut it down while I run inside. When I come back out a few mins later and start the car, the starter turns the car over and then continues to spin. if I turn the key back to ACC the car shuts off but the starter still spins and will start again with the key back in run. The previous owner told me to pull the starter relay to make it stop and that seems to work. I can start the car then get out and pull the relay, the starter stops spinning, then put the relay back in and it's all good. I've replaced the relay with a brand new one and the issue continues. Keep in mind this doesn't happen every time I start the hot car, but only sometimes at random it seems. Another side-effect I've noticed is that when this happens, the gas gauge on the cluster occasionally will show zero. The gauge seems to work fine if the car is key cycled, but still leaves me with a spinning starter. Another thing I've noticed is that when the car sits overnight or for a few hours, it takes longer to start the car. It will crank for 30 seconds or more before it starts. It's a strong fast crank and the battery is new, so I'm not sure if that is related. This long crank is consistent for every morning and every time after sitting all day at work.
Could this just be a bad solenoid on the starter? Or, does it seem more like a wiring issue?
Thanks for the help,