I found synthetic grease "stays" better than the petroleum products. I wash my flintlocks after shooting, with a toothbrush and in the bucket of water
I use for the barrel. I shake them off then blow of the excess water, wipe them down with a towel, then spray them all over with WD40, shake then blow off the excess
WD40, then wipe and replace in the gun. I only have to lube them once a year, cleaning them this way. They have never picked up any rust - never & remain lubricated for the year.