Traffic lights are important components of traffic systems, and perceptual tasks on traffic lights are crucial for intelligent agents on the road. Auxiliary countdown timers, providing the remaining time of the current traffic phase, improve the safety and smoothness of the entire traffic system. This work proposes a state estimation framework for countdown timer traffic lights. Time-domain information is adequately integrated into a variable transition Hidden Markov Model (VT-HMM), and our system provides optimal estimates of traffic light colors and countdown numbers based on noisy detection inputs. A dynamic state transition matrix is designed based on a 1-step transition logic and a probability of the number of transitions related to the current state sojourn duration. A recursive decoding method based on the Viterbi algorithm is proposed to update all the state candidates and select the optimal state chain. Extensive experiments evaluate the robustness and effectiveness of the proposed work. The performance boundaries of this system are also found under various input noise levels. The source code is available here: https://github.com/ShuyangUni/countdown-timer-traffic-light-estimation