In doing research in to the first words said on the surface of the various Apollo astronauts, I found there was no video of Apollo 16 and 17, at least until they had been on the surface for a while. Why is that?
The Apollo 16 Mission Report, section 9.8.2 explains
First extravehicular activity.- Following the first sleep period and normal preparation for surface activities, the Commander egressed slightly ahead of schedule. Because of the steerable antenna failure, there was no television coverage of the Commander stepping onto the lunar surface.
According to the Apollo 17 Mission Report, section 9.2,
The lunar communications relay unit provided satisfactory support from the lunar surface, and the ground-commanded television assembly produced good quality pictures at all times. Activation was initiated about 1 hour and 11 minutes after crew egress for the first extravehicular activity. Television coverage of crew egress was not available because the capability to televise from the lunar module was eliminated for Apollo 17 to save weight.
For Apollo 16, there should be.
Start of EVA-1:
119:02:43 Duke: Okay. (Long Pause)
[Charlie turns the 16-mm movie camera on and we see the left side of John's suit as he makes his way down the ladder. The jett bag is lying on the ground at the north edge of the LM shadow.]