I am running a cox regression model in survival analysis and I have a question about time-varying covariates. I have a covariate that describes subjects total waiting time (in days) by the end of their observation period. At the beginning of the study (t=0), all subjects were put on a wait-list. I have two groups of subjects: 1) still waiting by the end of the study and 2) waited and received help(aka stopped waiting during study). I am interested in whether subjects' waiting time has an effect on the probability of the event of interest occuring.

I am wondering whether I should treat this waiting time covariate as time-varying or not. If I treat this as a time-varying covariate, is this the syntax I should use? I modelled my syntax from the example in the Stata manual under 'Cox regression with discrete time-varying covariates'
stcox waittime, tvc(waittime) texp(.1*(_t))