If the skid becomes compressed due to contact, it is no longer in the down position and will that cause the light to illuminate?
No.
Within the PSEU there's a 36second time delay built in to the light and message. So unless you could perform a tailscrape that held the skid compressed for more than 36secs you won't see either light or message.
The light and message are there for tailskid position fault annunciation.
In short, there is
NO tailstrike warning system on the 767-300.
Just pilot "feel" or report from cabin crew or ATC.
.