Brightbore solvent will leave your trigger looking like it had bee's wax packed into it.
One of my brothers got a Bright bore cleaning kit with that solvent and the trigger of every bolt gun wound up like that.
It just runs down the bore and down the bolt and collects in the trigger mechanisms of 700s and 788s. It would probably do the same on a 582.
I have never had that happen on any of my rifles and I have a 581 with the same trigger. But I use Hoppe's #9 for a bore solvent.
>>>>FWIW I am thinking a lot of those Remington accidental discharges could be related to that style trigger pack gumming up.<<<
I agree with this. I have had to degunk several triggers of used Remingtons where the cocking piece was following the bolt closed. They all had old varnish and wax in the mechanism. All worked fine after cleaning up.