Lots of wax in those old amps, usually nothing to worry about. Sometimes you get a blob that melted out of hot transformer - I've seen that in 60's Vox amps besides other 30-40-50's amps. When you see that you know the transformer got overheated at some point. If it's still working then on with the show, and if not, well there's the evidence why.
Now, what's the function of the choke you mention. If it's a filter choke, 10 Hy sounds about right, then you'll want to leave it in place, or replace it if damaged. Rare to see one gone bad, but it does happen on occasion.
Some older amps have a choke wired across the speaker terminals (!) in an effort to "voice" the speaker. You can imagine . . . a choke there tends to look like a short circuit at lower frequencies. Seen these in 50's Premier amps mostly, but one might show up in a Gibson. If that's the case, I remove that choke. If the amp's owner insists for originality's sake to leave it in then it's a choice of leaving the choke in place for looks while detaching one of its leads, or leaving it wired in place. That's up to you and the amp's owner.
By coincidence today I'm having a go at a tweed "Gibsonette" with a pair of 6V6's driven in parallel not push pull. They did such strange things back in the day...