Fluid level is fine, since windshield spray still works.
I also checked the tube on the rear wiper arm itself, and it seems intact.

Know of any common fail points to track down?

Here is the weird part. When I disconnect the hose from the wiper arm nozzle, the water comes out.
When I connected it, and push the washer switch, there is a loud whining sound coming from under the hood, right in front of the dashboard.

Could the nozzle on the arm itself be clogged?

^ This

The tube could be getting pinched in the wiper arm. I have this problem. The tube is drying out and shrinking and now the pressure of the washer fluid just blows the tube off when I hit the rear washer button

Not sure about other stores, but Oreilly has two sizes of stiff black plastic evap line in the help! aisle, the smaller of the two (I forget the size) replaces that hard line in the wiper arm perfectly. I haven't had to find a replacement for the two soft pieces yet, though.

The weirdest thing happened with this.

The wiper arm hose wasn't the problem.
Neither was the nozzle. Not blocked.

When I'd press the switch, there was a loud chirping from right at the driver's firewall.
I kept pressing it and then fluid started coming out of the wiper arm again!

When the fluid was spraying, the chirping would trim down.

Fluid spray = no chirp.
No fluid spray = chirp.

Any idea what was chirping? Right under the driver's windshield on the engine side.
It sounded like it was coming right from the washer fluid cap area

up in the drivers side fender is the wash bottle. on the bottom of the wash bottle you have two pump motors. one for front, one for rear. they are small and easy to replace. best to replace when fluid is empty. just remove fender lining and reach up to the pump and pull it out. it is just pushed into a rubber grommet. if you have fluid in the wash bottle, it will pour out.

grab one or two from a junkyard first to see how yours comes out.

Sounds like you're tracking down your problem, but I was told there is a type of valve that stops the line from draining, towards the back of our XJ's. Someone told me to check that valve as the spring & ball bearing sometimes rust and stop the fluid from flowing. I think it's above the head liner.

My rear squirts don't work either, gotta figure it out one of these days.

It wasn't the hoses, nozzle, or switch. So, it must be the pump.
Yea, it sounds like it was the rear motor pump.

For now, my rear washer suddenly started working, and that chirping is gone.
If it comes back, and the motor dies again, I will replace the motor in the fender liner.

It knows...

Mine squirt straight back - great entertainment when you get a tailgater!

Lol, buddies old VW Scirocco did that back In High School. It did work when being tailgated.

I don't even have a rear wiper

Washer is working at full blast again....Weird.