As Jon said, the window washer system on the Tbird was certainly not one of its good features. As memory serves me, that system was mounted down by the generator and ran off the belt to it. It was usually one of the first things to fail and many in the old days just took it off. There should be a red water bag hanging on the drivers side of the engine well fairly close to the hood latch. It had a hose running out of it, that fed the spray nozzles in that grill in your picture. There were between the knobs for the windshield wipers. They screwed in place and were set up to spray the water on the windshield.
It might be possible to get the washer mechanism off a donor car. The bag is available and probably the spray nozzles also. You might email Eddie ~ EddieB1222@aol.com
who has a '60 Tbird he has been parting out. He might have a lot of things you need. Contact Don at Bird Nest also, at 800-232-6378 or email him at: firstname.lastname@example.org
He might have the parts you will need to put it back in original condition.
I looked to see if I have a picture of my spray nozzles in place, but I do not. I am going out to see Yellow Rose later today and will try to remember to take some pictures. However, I thougt I saw a screw hole in that screened grill section in front of the windshield. That is where, as I recall, one of the spray nozzles screws into place.
On the other hand, if you cannot find the parts, there are electric windshield wiper/washers out there that can be put in place of the manual control which is located behind your glove box. They will run you close to $300 US as I recall.
I hope this helps.