Mega-maxi-pedant alert:

This, and my being esteemed a pretty good rig-ite, that is, a jocular verbal satirist, supported my consequence in the society. [Benjamin Franklin]

Couldn't find a hard etymology* but, back where I come from, ryg or rig is Danish Creole for “back” or “held back”. A gelding that, none-the-less exhibits certain shall we say, ahem, 'related behavioral issues' is a “ridgeling” or simply a “rig.” ie: One or both gonads held back from the scrotum; a “false gelding” (cryptorchidism.) They can be a right frisky handful around the girls but it will never amount to anything.

Ergo, “rigite” or “ryg” for a quasi sex worker. Riggy, riggish, riggers &c for randy or horny. “Run-a-rig” is what b-girls in clip joints have been doing for centuries. Politicians and diplomats same-same.

*It may be closer to a “ship's rigging” than first appears (via ridge.) Too little to go on.