What type of relay/switch device am I looking for?
Apply the pulse signal through a capacitor and a diode half bridge to the gate of a mosfet.

This will turn the mosfet on as long as the pulses are coming.
The mosfet will be off when the pulse train stops (hi or low doesn't matter)
The pulse voltage has to be large enough compared to the gate threshold of the mosfet. The 2N7002 has about 2.5V threshold voltage and the top schottky diode eats another ~0.2..0.3 V. So the minimum peak-to-peak pulse height has to be at least ~2.8V for this to work. If your pulses shape is smaller, then another mosfet with lower gate threshold voltage must be used.
R29, R30, C26 are optional.
R30 can be placed to discharge the gate faster, when the pulsing stops. Without R30, the gate discharges slowly due to leakage, which can take several seconds. The smaller R30, the faster the turnoff.
C26 has the opposite effect, it increases the charge available at the gate node, making turn-off due to the leakage slower. It also makes the turn-on slower though. If you want instant turn-on within 1-2 pulses, then C26 should be well smaller than C25.
R29 is there to limit the peak current from the pulsing IO pin. If C26 is small or missing, R29 may not be needed either and can be replaced with a short.
The capacitor voltage rating in the schematic can be ignored, they should be able to work with the pulse voltage, which is usually low (e.g. 3.3 V), but higher voltage spec doesn't hurt.