One simple cure for your problem may be to perform the fogs-on-with-high beams modification shown at the bottom of this page: http://dodgeram.org/tech/mods/electric/headlight.htm
The modification is identical for second-generation Rams model years 1999-2002. The fog lamp relay does not turn on the fog lamps. It functions as an interlock, allowing fog lamp operation with low beams and preventing fog lamp operation with high beams. By replacing the switch in the relay with a jumper you will allow fog lamps with both low and high beams. By removing the fog lamp relay you will eliminate the path through the relay coil that is likely the source of your problem.
The modification is identical for second-generation Rams model years 1999-2002. The fog lamp relay does not turn on the fog lamps. It functions as an interlock, allowing fog lamp operation with low beams and preventing fog lamp operation with high beams. By replacing the switch in the relay with a jumper you will allow fog lamps with both low and high beams. By removing the fog lamp relay you will eliminate the path through the relay coil that is likely the source of your problem.