Hello rfrey1:
Comparing your opening post to your next reply, I see that I just assumed that the mushroom only was a GPS antenna. Nothing more. But by your next question, maybe there is more to the thing? Such as also being a NEMA device.
Anyway, mine was a mushroom type GPS antenna only that failed on my circa 2003 Standard Horizon 150 GPS + Chart Plotter. And the $7.50 eBay device was a perfect replacement (actually an improvement!). The original antenna and new antenna connect to my Standard Horizon display/head unit. Just a simple matter of screwing into the antenna input of my chart plotter. In my case, it's the chart plotter head unit, not the antenna, that then interfaces with other instruments and my Raymarine ST4000+ autopilot. One thing to note is that the GPS "antenna" units are more than just a passive antenna. Inside is a circuit board with micro chips that need a supply voltage to operate. In my case (and I suspect most cases) the supply voltage is transmitted via the 2 wire (center+ and shielding-).
Attached is a picture of the coaxial connector and wire of my generic eBay GPS antenna. There are several types of generic coax connectors. You will have to do your own sleuthing.
But if you have four wires in your connector to the mushroom then it is more than a GPS antenna and I don't have the knowledge to assist.
Hope this helps a bit your sleuthing towards a solution.