From my experiences, hunting with many partners over the years,
multiple lights at a stand is a plus, putting odds in our favor.
I have many examples, one over the top example being four of us killed 3 Fox on one stand, next stand we killed 2 Fox, all the time talking that this guys sees eye and that guy sees eyes and wait, there's another one.
I prefer to hunt with one partner, but that night was for kicks, the four of us hunt'n for fun.
Bottom line...multiple lights at a stand is a plus
I agree with 2223... be conscientious that you don't back light your hunting partner
Also, if partner is casting shadows (moving shadows) while scanning it may spook or halt incoming Fox.
or if partner is moving/walking without keeping light on incoming Fox.
These would be the 3 details that I would re-live with your hunt about 'what happened.'
If none of these details apply, then we may talk about 'why' Fox hang up on a good set up.