I did San Jacinto via the tram 3 weeks ago.
Idk about those particular trails you are taking, but the peak trail from the tram did have a water source a couple miles in from the tram. There is a little runoff creek that was flowing in the lower elev of the peak trail as well. Not sure how far these are from your trail junction.
Btw we all xp hikers prehydrated and brought 3L plus electrolytes. We went during the first heat wave but at elev temps were k. Air was still so dry plus being above 8K the entire hike, we all ran out a mile or two before the tram and were shocked – we had never run out before and sipped conservatively. I advise bringing 5-6L if you can carry it plus electrolytes and a filter for backup. Have fun!