I'm assuming that the keytar in question is set up to do modulation (vibrato) on the same controller number as the mod wheel on the Trinity/Triton -- it should default to that.
That it is not causing vibrato could be an indication that at some point it was assigned to a different control number... so my first suggestion would be to see if there is a reset/default setting on that controller.
Second - the question of "where is it" - is yes, the general set-up for the Triton and Trinity are very similar. The vibrato as far as volume goes is located in the AMP section of a program - you should see a modulator or control assignment box that allows you to set up a LFO (low frequency oscillator) and which can then assign it to JS+ or another control.
Pitch modulation allows a similar control routing(LFO @ value/rate 'X' to controller 'Y'), though with you might want to keep the ranges pretty low.
Either or both of these aspects of vibrato can be assigned to the JS control.
REFERENCE IN MANUAL: Alternate Modulation Source (AMS) assignments, ranges and controls, as well as LFO and controllers. You probably won't find vibrato, per se, except as a possible effect in the IFX section (think surf guitar).
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If you built your patch up from an INIT program then the starting values may be either OFF or NO CONTROLLER SELECTED (which amounts to the same thing).
You can copy many settings, FX and other parameters from other patches in the pull-down menu (upper right corner) on many edit menu pages - that might speed the process.