2 dash lights come on and off (noticable pattern)

[420samurai]

My '95 Grand Am sounds like its running fine. The Check Oil light will come on after I leave the car setting for about a day. When I reset the lights, it won't come on while I'm driving. Occasionally it will come on the very next time I start my car, but usually it's the next day. The Service Engine Soon light will only come on when I'm parked and not driving. Like when sitting in my parking space listening to the radio or pulling over to the side of the road to adjust my mirrors, etc. When I start driving, it will turn off after a couple seconds.

 

I'm fairly new to cars. Recently graduated HS and I only took one year of Automotive class. I'm not sure what the issue could be, sometimes I think the car could not be getting enough oil pressure when idle. But sometimes the check oil dipstick (Which always checks out fine when checking oil level) sometimes smells like gas has mixed in with it. The oil has also been changed within the past 2 months because of this issue so I don't think another oil change is needed. The fuel filter has also recently been changed.