I have seen this (or versions of this) old butterfly splice cue with the pin in the shaft a number of times before. Each time, the identifications were guesses at best.
It may be a three cushion / carom / balkline cue - a lot of these types of cues had the pin in the shaft instead of the butt (the latter being the most common in today's billiards and pool cues).
If it is a Brunswick cue (which I am very doubtful of), it likely wasn't made by them. They often contracted out their cue work.
I would bet that recessed nameplate spot is done by the previous owner.
They aren't worth much of anything, usually selling for ~$100, give or take $50, and they don't hold any specific collectible value (unless they were in like-new condition - and even that doesn't bring much of a premium).
Here are the other ones like yours I have seen around:
I think a few companies made them to be sold as Brunswicks, including Schaefer IIRC. They are not rare, per se, and don't tend to hold much value, but are pretty neat if you ask me
There were a couple for sale on eBay over the years, and in all cases the sellers guessed that they are old Brunswick cues (as they always do when they have no clue what it is). Again, they may or may not be.
I am only showing this first one as it has what is obviously an identical joint type (also with pin in the shaft) to the one you pictured.
BRUNSWICK BUTTERFLY SPLICED CUE 1950'S TITLEIST CUE CUSTOM CUE OLD CUE
And this other one looks similar to yours as well.
ANTIQUE BRUNSWICK BILLIARD BUTTERFLY SPLICE POOL CUE