Really? The overtones always seem to be there through my amp, but muting seems to have fixed it. I use a wristband and it's easy to slide it quickly up to the nut so the opens are not muted. But tapping on my squier jazz isn't a problem through an amp, I don't even need the mute for it, it's just my yamaha...
Hi there, I hope I can help, I've been tapping instruments since I was born, and got to embrace some good practices that may help you:
- Low action definitively helps, not just because it will make your play easier and the whole movement more effective, but also because it will reduce the overall noise created by the action of your "tapping hand" on the strings. When you tap, both sides of the string resonate, one going to the neck and the other going to the bridge. By plugging into your amp, you overcome the "finger to neck" sound, but it is always there. If you have lower action, the string resonates less (and you need less energy to tap the note), so less noise will give you a clearer sound.
- the rubber band in the neck is, to say it gently, a temporary solution (not very elegant) that will bring you problems later. Tapping is just 1 technique among others you may want to use while playing, and given a particular tune, you may want to combine tapping / slapping / muting / chords, whatever. Putting a device in your bass that supports one thing but disables others may be very limiting.
- When tapping on a bass, beyond the advice you have received already, I can recommend that you use your (if you are right handed) left hand's index finger as a capo to lower the strings around the section you want to tap, sort of temporarily lowering the action to the lowest, and use the rest of your available fingers to play. That finger should also be your main muting device.
- On your tapping hand, don't be scared of using all your 4 fingers to reach across the fretboard more easily. The pinkie will be a pain at first, but after a while you will see that it helps a lot. Try always to play as vertically to the strings as you can with the tip of your fingers.
- Heavy strings may give you more sustain, but they require a lot of energy to tap on. I would suggest light, new strings to get the most out of your sound.
- So you get some progress from the get go, if your Yamaha has some equalization capabilities, put all the bass/mids to the max and reduce the treble to the minimum. Bring the balance between pickups to 50/50. This sound will not be the way you want to sound, but may clearly show any muting problems you need to address. Once you feel your are ready, bring all the eq to their neutral position and put the treble to the max. That will help you find any non-desired harmonics you are creating and thus allow you to correct your technique faster.
- Move around, don't stay with your hand just between frets 9 and 15.
Hope it helps. Cheers