Pilot hole for joining 2 2x4

Hey all,

I’m making this shelf for my garage. I’ve got #8x3" screws for joining 2x4’s, the screw box recommends 5/64 size pilot hole. However the 5/64 bit I have is only 1.98" long so it wont go through both 2x4’s (for the 2x4 acting as brace and 2nd one on top acting as shelf). Photo for reference From the bit of research I’ve done, only the bottom 2x4 should have pilot hole of 5/64, the top one should have a larger hole (maybe ~ 5/32) for better clamping force. So, I’ve been looking for longer 5/64 drill bit but cant seem to find it. Other option I’ve been thinking of is using 5/32 bit on top 2x4, that should leave a mark on the bottom brace 2x4, then I can drill there with 5/64 bit. But this will be quite a bit more work and more error prone.

So any recommendations? Does longer 5/64 bit exists? Most sets I’ve found online also include a short 5/64 bit, like this