Rarely go into the alley, so this one came as a surprise. And generated some dismay, too--my neighbor's fence isn't all that sturdy. Opinions?

Yep, definitely looks like Four o'Clocks (Mirabilis jalapa) They can get quite tall here in Florida and I'm sure in Texas too.

I haven't seen them grow like that but we don't have long seasons. I was wondering if it is some kind of a honeysuckle......

Yep, Four O'Clock.
As for the fence; if good fences make good neighbors, um, well, good luck with that.
Maybe once you have your yard looking really good your neighbor won't need the fence anymore.

May be Honeysuckle ... I can't see the leaves real clearly but the buds and blooms and growth habit sure remind me of Mirabilis.

It has definitive stems rather than vines. The height surprised me. So. Probably Four o' Clock. When it cools down next week, will go cut off the part draped over the neighbor's fence. The database says it's beneficial for a lot of critters, I'll leave the rest for them until it freezes.

Thank you, everyone.