My little Honda crx has a tendency to jump the RPMs from 1500 to 2000 and back to 1500 constantly when the car is parked or on neutral. I have noticed that it even does when the engine is warm and the RPMs are lower. I have also replaced the pump but it is still doing the same thing. What causes the engine to do that and how do I fix this problem. Thank you for your time.

I would check the Throttle Position Sensor, and verify smooth movement with analog meter as you move arm.

Here is a fairly complete list of items to check:

. Check/replace Idle Air Control (IAC) Valve.
. Ensure all vacuum hoses and connections are good.
. Ensure no leaks around throttle body or intake manifold.
. Inspect for faulty Alternator FR Signal--have alternator inspected, if idle speed fluctuates with electrical load. The FR signal (WHT/RED) communicates to the ECM how "hard" the alternator is working to meet the electrical demands of the car, including the battery and any loads which aren't monitored by the ELD. This signal is a square wave that varies in pulse width according to the load on the alternator. The ECM puts a 5V (approximately) reference voltage on the wire. The voltage regulator will drop this signal to approximately 1.2V in proportion to the alternator load.
. Clean main ECM ground on thermostat housing.
. Reset ECM, by removing Back Up fuse in the under-hood fuse box for 10 seconds.
. Check idle speed adjustment:

https://www.askmehelpdesk.com/cars-t...tml#post219948

. Replace PCV Valve:

https://www.askmehelpdesk.com/cars-t...tml#post819639

. Substitute a known-good ECM. If symptom goes away, replace the original ECM.

I added the material below to the Sticky, because of your question:

https://www.askmehelpdesk.com/cars-t...s-46563-7.html