The delay time to breakdown of a cold-cathode thyratron with a trigger unit based on an auxiliary steady-state low-current glow discharge was studied experimentally. The device was connected into the electric circuit according to the circuit of a classical thyratron. The main experiments were carried out at low working gas (deuterium) pressures and high anode voltages of about 40 kV. It is found that, during the triggering current pulse or commutation of the main discharge current, the auxiliary discharge in the trigger unit passes from the stable segment of the current-voltage characteristic into the regime with a reduced operating voltage. Spontaneous reverse transitions from this regime are also possible. On the other hand, the initial conditions of the auxiliary discharge affect the delay time to thyratron breakdown and lead to the jitter in the total delay time to breakdown relative to the triggering pulse. The total delay time amounts to 100 ns, the jitter in delay time being within 15 ns.