Randomly won’t start after short trip. For example,I stop at store after work- 15 minute drive- in store for 20 minutes, come out, car won’t start. Let it sit for another 20 minutes and then it will start but RPM gauge reads zero when car is driving- at this time it will not accelerate over 35/40 mph. Sometimes it starts fine after the 20 minute wait. It is very random.
I’d guess the first step is a shop assessment of battery and charging system. Diy’er version: Before first start of day battery should measure about 12.6 volts; then immediately after starting engine, 13.5-15.5 volts. I did this test the other day on my Corolla, hadn’t been started in a month, measured 12.4 volts before first start of day, cranked more slowly than normal but started ok, then measure 15.0 volts once engine started.
Fuel system problem can cause hard starting after 20 minute wait, but those don’t usually affect the RPM gauge. That symptom points to an electrical system problem of some sort. Best to sort that out before considering the fuel system.
Is the check engine light on? Have you had the error codes read?
Based on the lack of RPM reading, I’d guess the camshaft position sensor may be failing.
The crankshaft position sensor may be failing.
The tach signal comes from the crank sensor.