For patients on T4/T3 combination therapy for management of hypothyroidism is there an indication for monitoring T3 levels and if so, what is the appropriate timing (trough versus peak) given the pharmacokinetics of liothyronine?

For patients taking a combination of T4 and T3, in my opinion, there is no need to monitor T3 levels. The aim is to keep the TSH in the desired range. One may want to keep the TSH level somewhat higher in the older patients compared to the younger patients.