I haven't considered game mechanics for the drug as yet, but as the effect can be detected by McCoy's equipment demonstrates the effect radiates from the user.
Further, based on the demonstrated mental lapses of judgement and trains of thought, the subconscious drool factor exhibited, non-users are clearly affected and with diagnostic accuracy by the briefing room's computer analysis of the male board members.
Spock is bemused by Scott and McCoy in the transporter room and will have never seen them act that way ever before or again.
Mudd is likely not immune, but forewarned is forearmed. He also tells the girls to 'save it' on Spock suggesting the user can consciously target the effect on one or lapse concentration and affect all in a 15' radius or some such.
Distance, focus, dosage, duration, wax/waning of power. Is it akin to lead acid battery that slowly drops over life time or a lithium battery that holds power until the end and drops precipitously? The show demonstrates a hard crash in the cabin scene on looking for where Mudd hid the drug. It could be that at the end moments, the user can use some 'will power' to make it out of sight and crash in private so no one sees -as Eve has at Childress' on his awakening. This would be a penalty to the user's long term health akin to the rules on usage vs. abusage of psi drugs.
The women in the cabin scene crash hard and become desperate as their 'natural selves' take over. We don't see Eve's second crash. Duration would seem to be on the order of many hours to days. Two options are 5d10 hours averages at 27.5 hours or perhaps 3d10 avg 16.5 hours. Onset is near immediate in 1d10Turns. Crash is over 1d10 minutes and may be inducing (minor) psychosis during transition, possibly becoming violent in extremis.
As to what the drug does to the user.
As Mudd suggests, women typically are going to gain on the CHA (though CHA is not representative of looks, yeah yeah). Whereas it sounds like men typically it's going to mod the STR. Or END... It's likely best defined by Mudd as giving you more of what you have least of.
A frail fellow may gain massive END, while a weak though solid END might gain STR. Meanwhile a clumsy fool of any stripe will gain DEX. The unlucky will get lucky while the fearful become COOL and the stupid become genius thus drawing admiration that way. In the case of Mudd's Women, their self-confidence spoke through CHA (though CHA is not representative of looks, yeah yeah).
Likely some 'natural skills' are gained, possibly such as seduction or carousing for CHA as it appears to lower the self-consciousness people have, instilling personal confidence. For INT maybe inherent understanding of physics, warp theory and Sm Eq Tech or for LUC there is inherent understanding of gambilng, gaming, trade and commerce and the like.
The abusage rules are harsh and the venus drug may be in a lesser-harm class for the seeming need to take more as demo'ed in the cabin. Eve is later seen in post-crash doldrums per abusage rules, irrc.
The Venus Drug appears highly addictive as all PSI drugs are. Breaking the habit is best done by not starting.
To fully explain Eve's final transformation, it could be that there is latent PSI energy that slowly burns off and in this case the placebo effect was enough to kick the Venus off one last time for a few last minutes. Instead of 3 or 5d10 hours duration, perhaps the latent placebo is 3 or 5d10 Turns or minutes.
3d10 is likely the more accurate range.
Perhaps I should consider a 'latent placebo' effect for any future tweaks to the PSI rules.