Linking Two Gene Activity via Transcription Factors similarities

Let say I suspect Gene A and Gene B of mouse share similar Transcription Factor.

What should I do to prove this?

From my limited reading, I manage to obtain a list of TF from PROMO website for Gene A and Gene B by simply input 1kb sequence of both genes 5′-region.

How should I go on to prove this?
What data I need or relevant enough to put in scientific publication to justify my suspicion?

*Background Information
Limited metabolite data seem to suggest Knock Out of Gene A increase Gene B pathway activity. Of course best way to prove this is gene expression of these 2 genes. But with limited fund and time, I try to explore other possibilities first.

Thank you again everyone for reading helping me to understand bioinformatic area!