It's been a few years ago but my experience at the west camp was great. We had the place all to ourselves in November.
Nice sites with lots of mesquite trees for shade and several war surplus tank trailers for water. Clean pit toilets.
My understanding is that the locals have first dibs and it may be closed if there's a tribal function, but those are very infrequent.
There's a tribal office at the turnoff from the road to the campground although it is frequently unmaned.
A couple of indians checked us out while we were there in the off season. Things were pretty informal and the method of payment is push the cash thru the slightly opened office window if no one is around. It was 10 bucks a night then.
The hike up from that side is really pleasant also, thru a forest of the tallest Suarros (40 ft'ers)I've seen anywhere and with as many ripe tunas as you can eat if they are in season.