No, I didn't test them. I cracked them a while back so they needed replaced anyway. I bought the speakers you suggested, the:

Pioneer A-Series Standard TS-A1671F, 3-Way Coaxial Car Audio Speakers, Full Range, Clear Sound Quality, Easy Installation and Enhanced Bass Response, Black and Gold Colored 6.5” Round Speakers

OOOh, didn't know that about the foam! TY. Is this what you're talking about?
(I know you said "perimeter," but when I typed in "Speaker foam," that's what came up-a disc)

Well, I'm hoping by Wednesday. Will let you know :)

​​​​​​​So you knew they were the problem all along?

LOL, no. I just turned the sound down a bit and dealt with it. (I would have kept doing that too)
As far as knowing it was the problem, no again. I would not have made the connection to the blinkers, the stereo
going out, and speakers being the problem. (PulpFriction did that, thanks) I truly thought it was the stereo/radio itself.
I came here to ask the guys that really have a better idea of what
might be happening with the sound and the blinkers.
Since they are cracked, it can't hurt to start with them, since they think it's the problem.
Cracked speakers still play music/make sound, so I didn't make the connection. I hope I've explained my ignorance enough.

I was talking about some Frost King self-stick foam home insulation for similar results to the Amazon product, which looks good, but is costlier. Prolly worth it.

OK. So I'll go with the discs. TY.

I promised I'd post when this was taken care of. I finally was able to have my mechanic replace all of the speakers and other components yesterday morning. I've driven it about 70, 80 miles since,
turned the car off and on about 10 times and so far, so good. No intermittent stereo going off and on, and my blinkers work with sound.
Of course, this is not time-tested, but I'm confident I was given good advice from Pulp Friction so I feel good about this.
The other plus? Stereo sounds wonderful. :)