Does it even have a rectifier? Headlights are not specific, they don't care if the current is alternating or not. If there's no battery or DC accessories it might not have a rectifier at all.
If the gizmo can accept AC then it might be that all you need is a TVS. Alternators are very noisy and the spikes can be pretty substantial and the bike is blowing out the rectifier inside the power supply. Things like this are often cumulative, so it'll work for a while but after some period, say 50 or 100 hours, the 1ms long 200V spikes just wear out parts to failure.
I would just hit Radio Shack, a couple of diodes and a couple of caps potted into epoxy is going be cheap.
'91 Pickup - Imelda / '08 Tacoma TRD - Donna
'09 Kawasaki KLR650
'98 Rhygin Juke SS / '12 Gunnar Rockhound 29 / '16 REEB Dikyelous
"Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty. Nobody is able to achieve this completely, but the striving for such achievement is in itself a part of the liberation and a foundation for inner security. " --Albert Einstein