The 767-300 has a 'tailskid' light, but not a specific 'tailstrike' light. The 'tailskid' light comes on if the position of the retractable tailskid does not agree with the landing gear handle position.
That said, yes, it would probably come on after a tailstrike if the landing gear handle is down, since the 'up' position of the skid now disagrees with the 'down' position of the gear handle. In this plane, the most common time for a tailstrike is on landing, so if you see the light on after touchdown, most likely you did scrape the skid.
However, at Hawaiian when we first got the 767's, we had a few incidents where the skid had obviously touched the runway (scrape marks) but the light didn't come on (not hard enough to move the skid). Maintenance is required to do an inspection anyway, but there wasn't a sure-fire way to know after each flight whether or not it was a new scrape, or an old one. They first tried painting the bottom of the skid, but that came off with the coffee and hydraulic fluid that always seeps out along the bottom of the fuselage. The final answer was to wrap safety wire around the base of the skid, and make it part of the preflight inspection. Wire there = no strike. Missing wire = inspection.
One smooth landing is skill. Two in a row is luck. Three in a row and someone is lying.