Dave,
Few possible solutions:
Guitar amp : Since you mentioned this is the most obvious, let's start here. I would suspect (3) sources here:
Guitar, amp or cable in that order of importance IMO.
1.Guitar : The magnetic pickups are very susceptible to picking up RF noise and depending on the design, they may be noisy themselves if you have a no-hum cancelling single coil like a Strat. What guitar do you have and what is the pickup configuration? Are you pickups single coil or humcancelling? I play an original 97' maple body Parker Nitefly which originally had an S/S/H pickup configuration in the pickguard. I played a Dimarzio HS-3 for years and wired my guitar to only use the neck pickup. I installed an on/on/on switch and can play the pickup in series coils, parallel coils or split the windings for true single coil. As soon as I split the coils the noise factor goes through the roof. It is so bad I never play the middle position, just series or parallel. Then I discovered this:
http://www.wdmusic.com/parker_nitefly_m_pickguard_nfm_8228bk.htmlWD music makes a H/H configured pickguard for my guitar. I immediately ordered a Seymour Duncan Pearly Gates neck pickup and kept the on/on/on switching. I then ordered (4) of these :
http://www.partsconnexion.com/spoints-70605img.html1 sheet applied to the entire back of the pickguard, then another part of a sheet for the bottom of the electronics cavity, and then the sides of the cavity. I would recommend a PEC 250K pot, carbon and silent then star ground(common) everything; bridge, pickup selector switch and output jack to the volume's grounding lug. Use a test light and check for continuity through the bridge(and subsequently the strings)...