I have a 32" Sony something or other. One of the very last ones - HDMI port and does 1080i or 720p. What a find! 30 dollars, and about killed myself getting it in the house.
The plan is to have all the light gun systems hooked up to it. Being able to get 1080i out of a PS2 while having the light gun work is a challenge I have not yet surmounted.
Unfortunately, you might have trouble with light gun games. Some of the HDMI CRTs do some video processing that adds video delay. :(
If you're US based, you would probably use component video (YPbPr) to connect to your 1080i display; you can hook a ps2 light gun to the Y cable (usually green) and it should work if everything else is cool.
Thanks for the tip! I was not very far down this rabbit hole yet.