How to interpret the interaction term of a time variable and a time-varying variable? As a statistician, I was given a task to fit a mixed effects model where the right-hand side independent variables include a time variable, a time-varying variable, and the interaction of the time and the time-varying variable. I do not quite understand the model specification and am not sure how to interpret the results. The mixed effects models I have come across usually only use baseline covariates (i.e., covariates at time = 0) if time is included in the model, and I know how to interpret the interaction of time and the baseline covariate.
Can anybody help me understand the model specification with the interaction of time and a time-varying variable?

This is similar to having time-varying covariates in proportional-hazards survival modeling. The inherent assumption is that the association of the independent variable with outcome at a given time only depends on the current value of that variable at that time. The past history of that variable doesn't matter.
The interaction with time just allows the association of that independent variable (whatever its current value) with outcome to change over time since the start of the study. That isn't fundamentally different from any interaction term in a regression, as @Alexis notes in comments.
Whether that type of model makes sense in terms of the subject matter is another question. You might want to discuss that with those gave you this task.
