Options for getting into the park questions answered:
You have no north mountain reservations and no tour set up:
There are 10 north mountain spots that cannot be reserved. To claim one of these spots show up as early as possible (before 8 a.m.) at the park front gate. The earlier the better your chances at getting a spot. Sometimes Tours that rendezvous at the front gate will have open spots that you can fill as well.
At 10am all of the unclaimed north mountain reservations are given away to those waiting at the gate. Sometimes it is advantageous during the less busy times to show up at the park around 9:30am - 10:30am to claim these unused North Mountain reservations.
You have North Mountain reservations:
This is the easiest option for getting onto north mountain. These reservations fill up several months in advance and are obtained by calling (512) 389-8911. These reservations can be made up to 90 days in advance of your arrival. With these reservations you can drive to the office and gain access to North Mountain. Make sure you arrive before 10am or call the park front desk at (915) 857-1135 to let them know you will arrive after 10am.
Organizing a volunteer tour (the cheaper less reliable backcountry option):
Call the front desk of Hueco Tanks State Park (915) 857-1135 and let them know the date of when you would like to do a volunteer tour. They will contact you if someone picks up the tour.
Organizing a commercial tour is much more reliable than a volunteer tour. These are more expensive but you can communicate your needs with the guide directly and have a much more solid plan.