FWIW, I've actually purchased and used time delay relays modules for our club's use on accessories. We had a problem where certain accessories either needed short one shot timing and others that needed longer minimum duration timing in order to not get stuck or malfunction. By putting the relay modules in between the user buttons or track sensing sections, we can eliminate malfunctions of certain time cycle based accessories.
Fundamental point- knowing what module you buy, what it's requirements are (inputs and main power). And example here is one with a micro controller needs constant logic power to run the electronics. Some have built in regulators, some have even AC input capability, you have to know again, what it needed given you have an AC power source, and your sensing track section could also be AC, so it kind of matters. Then there are other super simple time delay modules with cheaper and less complex circuitry with no microprocessor, and so they can just be a power on and a set delay with a variable potentiometer to set the delay. The key is, they still need AC to DC conversion, and still have a limited input voltage, so hence the extra external AC to DC conversion and voltage regulation.
If you know what you are doing- sure, buying the cheapest possible time delay relay, buying or building the AC to DC and voltage regulator can save you money, but has prerequisite required knowledge.
Personally, I prefer the microprocessor based ones when I need an accurate fixed timed output or special sequencing, and as such, it likely has a regulator onboard, and as many inputs or outputs as needed, and being a microprocessor, can even do special functions, lockouts, and interlocks as required by your needs. Again, key here, if it has the LED display, buttons for programming, then read the details, it likely needs constant power and thus the wiring is completely different and may require a voltage regulator, or AC to DC conversion. Going even further, will the sensing inputs handle AC track voltage? All the kind of things you have to know and work out before buying- let alone wiring one up.
As an example from Amazon, a 2 input module since if I understand it correctly, you need 2 different possible inputs? I'm not saying this is the ideal module, just an example of what is out there.
https://www.amazon.com/NOYITO-Progr...me+delay+relay+2+input&qid=1613946897&sr=8-40