I have the Colt 6920 with the side sling bracket/swivel.  I want to mount the EIZetta light mount, which would not work with the side swivel mount.  Once I remove the bracket, I would need to drive out that beveled pin holding in the swivel. It appears to be the same basic pin as used on my CAR-15 and 6:00 swivel holes. My question is that once I remove that swivel pin, can I re use that same pin to mount in the 6:00 swivel holes?

Typically the swivel is mounted with a rivet (see Quib's drawing).  While you could remove the sling swivel and mount with a new rivet, might be easiest to just get a couple rivets (extras are useful on bad days ;-) and a new sling swivel.

Now if your existing side mount uses a roll pin to hold the swing swivel on, then it may or may not be the correct length and size to fit the FSB lower mount, however, I never trusted a roll pin in this location and have see them come loose on clones (does let the rifle fall if in use at the time ;-(

rivets are a one time use item.
roll pins i have used more than once.

Thanks for your answers and diagram. It is indeed the rivet I am referring too, and it does look like a one time part. The M4 and my old CAR-15 appear to use the same rivet size, but it looks like I will need some spares. I will wait until I have more to order, otherwise the darn shipping might cost more than the rivet.