So my recent American pale ale has finished the most active part of its fermentation (4 days, and bubbling has slowed way down), which was carried out at 66 +-3 degrees F. So it is now best to raise the temperature somewhat as it finishes or leave it where it is? I ask because this is is what Jamil Z. and John P. recommended for lagers on a Brew Strong podcast. So I am wondering if ales might also benefit.
It would. I normally keep them cool till they slow, or until airlock activity is minimal, and then allow it to warm up slowly over time for a few days. I think I've read that it helps rouse the yeast to finish cleaning up after themselves. I do it out of just being lazy and not wanting to continue to keep it cool, or take up precious space.
Raising the temp for lagers is for 2 days or so for a diacetyl rest before the lagering period. However, I have read and heard about a lot of brewers raising the temp at the end of fermentation for ale yeast as well.
Raising the temp for 1056 will make the rest of the attenuation and cleanup happen faster. So if that's important to you, there's the benefit. But as far as taste goes , I don't think 1056 needs a temp bump, though it probably won't hurt.
A lot of guys do raise the temp a few degrees at the end of fermentation for ales. As others have said, it's probably more common (and more needed) to do this with lagers, but it might get you a little more attenuation and/or cleanup with ales, or at least speed things up. In this particular case, 1056 is so fast, so clean, and such an overachiever attenuation-wise it's probably not needed, especially on a pale, which I assume was probably lower OG. Cheers!