Anyone have a light gun work on their CRT HDTV?

I bought a Sega Saturn with a stunner and the stunner doesn't work. The game acts as if I'm pointing the gun away from the screen and only rarely does the game register me firing at the screen(and it's not accurate). Is my light gun bum or is it the CRT HDTV too different than what the stunner was designed for? The HDTV is Sony KV-30HS420.
 
Traditional light guns only work with standard def CRT TVs. They won't work with standard def LCDs, high-def CRTs, or CRT computer monitors hooked up to standard def TV tuners.
 
Damn. I knew light guns don't work on LCD/Plasma but I didn't know it mattered between different types of CRTs.
 
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