I'm not the world's foremost expert, but those look like longframe 1/4" patch bays. Your two data points (former radio station equipment and sorta 1/4" plug) would seem to confirm it. Longframe connectors look like regular 1/4" connectors but with a smaller head. They're big versions of TT connectors (or the other way around, I forget) and they're not compatible with normal 1/4" stuff. The smaller head makes for bad contact in a normal 1/4" jack and the big head of normal 1/4" plug will deform the normalling contacts in a longframe jack. Or so I've read.
I just bought two longframe ADC patch bays that terminate via short snakes at a plate of punch block terminals off eBay for a pittance to use as mic line patch bays since my Neotek Series IIIc doesn't have mic line patch points on the built-in TT patch bay. I also made some longframe cables for myself, though you can buy them pre-made for about a buck more than the parts cost.
I used
Canare L-4E5C mini Star-Quad cable and
Neutrik NP3TB-B connectors. These are $0.33 per foot and $4.99 each respectively from Markertek. The mini Star-Quad is a bitch to work with (braided shield plus four teeny-tiny wires) but is good quality stuff. If you don't want to spend a long day watching
Band of Brothers (again) and breathing in lead fumes, I would recommend just buying pre-made ones.
Best of luck,
Dan