Is on call pay for tow truck opperators required in ca?

Whether an employee must be paid for "on call" or "standby" time away from the employer's place of business dependss on whether the employee is "subject to the control of the employer" during the on call time period or rather is free to engage in personal pursuits, subject only to the requirement that the employee can be reached if needed. To make this determination the courts look at the restrictions placed on the employee including whether:

there was an on-site living requirement;
there were excessive geographical restrictions on employee's movements;
the frequency of calls caused undue limitations;
a fixed time limit for response was overly restrictive;
whether the on-call employee could readily trade on-call responsibilities;
use of a pager/cell phone could lessen restrictions; and
whether the employee actually engaged in personal activities during such time.

For further information, here is a link to a site that will be of help:
https://employment-law.freeadvice.com/employment-law/employment-law/california-oncall-work-policy.htm
 

No, they do not have to pay you for stand-by time, since you can do the vast majority of tasks, chores, recreation (sleeping; any chores around the house; cooking and eating; using the internet or media; socializing; shopping locally) that you could do at home, locally, or potentially by driving the wrecker/flatbed to where you are going, so you have it with you. This is sufficiently your time, so that they do not have to pay you. That does not mean that it's necessarily a good job or situation, but in our employment at will system, the usual rememdy for not liking your job is to seek another one.