The use of telemedicine has increased rapidly over the last few years. To better manage telemedicine visits and effectively integrate them with in-person visits, we need to better understand patient behaviors under the two modalities of visits. Utilizing data from two large outpatient clinics, we take an empirical approach to study service incompletion for in-person versus telemedicine appointments. We focus on estimating the causal effect of physician availability on service incompletion; physician availability is likely to affect the likelihood a patient leaves without being seen behavior but only for patients who show up for the appointment. That is, physician availability should not impact the likelihood of patient no-show. We introduce a multivariate probit model with instrumental variables to handle estimation challenges due to endogeneity, sample selection bias, and measurement error. Our estimation results show that intra-day delay increases the telemedicine service incompletion rate by 7.40%, but does not have a significant effect on the in-person service incompletion rate. This suggests that telemedicine patients may leave without being seen when delayed, while in-person patients are not sensitive to intra-day delay. We conduct counterfactual experiments to optimize the intra-day sequencing rule when having both telemedicine and in-person patients. Our analysis indicates that not correctly differentiating the types of incompletions due to intra-day delays from no-show behavior can lead to highly suboptimal patient sequencing decisions.