That's what my grease-hole is primarily used for: holding the tallow for sealing up the pan, and making a dam to stop bbl gutter effect from tipping skyward, lastly for lubing a patch if my prelubes go missing or become unserviceable.
Don't miss the underside of the cover either--wiping up the lock after a shot.
I learned this the very first day I hunted with a flinter:
Finally got that sucker together and shooting and it wasn't quite done, but ready enough for a hunt. I was completely amazed HOW EASY it was to penetrate tangles and bush and handle such a long gun in my woods. Actually found it easier than toting a scoped, sling-equipped carbine--with their telescopes or slings or slung-mode bbl snagging on stuff all the time. The long-rifle, in-hand just slipped right through any spot I could maneuver my 6' frame no problem. What I was experiencing was so different than all those laments about "tight cover" and "long rifles" so I was focused on that. THEN, after a few hours of this slipping and sneaking around, I finally thought to open my pan.
It was empty. The wind and my casual handling of the gun had let all the fine powder slip out the tiniest gaps. It was dry and windy that day.
Since then I grease/seal the pan, wet or dry or windy or calm. Don't care. Tallow is cheap. And I started priming with FF. Now it's always there, every time I check. Heck yeah, I check. So happy I didn't get a shot on game that first day