I have a 2001 Explorer (4.0L 6V SOHC 4WD) with an erratic oil pressure gauge, which causes the "Check Gage" light to come on and eventually go off. I've done a search in the forums and found that it might be the oil pressure sending unit. Where is the unit located in the Explorer? (I've done a search and found the location of the units for other model trucks and SUVs but not the 2001 Explorer.)
I once had a Thunderbird had a similar problem. The "Low Oil Pressure" alarm kept going off. I replaced the sending unit several times, then found out that Ford had a service bulltein that recommended an in-line resistor be connected to the sending unit--Ford part. This was a simple and inexpensive fix to an irritating condition. The sending unit required a special socket, available at Sears or Pep Boys, etc. No trouble replacing that, either.