Lionel 253 Block Signal Light Issue

Since both signals are behaving the same, I would say a wiring error. You are using the instruction sheet to wire to the track I would presume. Olsen's online library has internal wiring if needed. Don't forget this signal use's 6 volt bulbs, #12, not the standard 14 volt #19 

I'll have to check about the lights, but they are both wired the same as depicted in the wiring diagram online: ground wire to terminal C, hot wire of the insulated block to terminal B, and hot wire to normal loop to terminal A.

The red light should go out, as it is controlled by a contact.  But the green light depends on the the motor resistance being low enough to drop the voltage across the bi metallic strip heater to near zero to go out. Proper operation of the green lamp would depend on having the correct lamp, a motor with low enough resistance, and the heater having high enough resistance.   As I recall the green light may never go out, it just gets brighter and dimmer.  Try the signal using a larger locomotive or even a twin motor locomotive and see if you get better results.  

Here’s it in action with my Lionel scale Hudson from 1990 with an AC Pullmor motor. So, it might be the bulbs in question if this is to go.

How are you insulating the center rail?

The rails are homemade insulated center rail sections made from older Fastrack that I cut the center rails in half and shaved a bit off with a Dremel tool to ensure the rails aren't touching each other. The insulated section is about 2 10" sections long.

OK.  So not matter where the stop control lever is adjusted, the lights are the same brightness? If it has the correct bulbs, I would try an experiment with regular tubular track. Try a test oval with the insulated section. Just to rule out anything strange that could be happening with fastrack.

I wounded of the resistor in the base of the signal is open. That would put the two lamps in series, so they would come on at the same time.  The design is this signal is typical of Lionel’s mid 1950 design in where they used metal frames and bus bars in the electrical path. Assembly was by tubular rivet or speed nuts. These connections tend to loose conductivity over time. They may need to be disassembled and cleaned or shunted with solder.  Also, sometimes just spraying the connections with DeOxit D5 will restore conductivity.   A high resistance connection would have the same effect as an open resistor. 

I think disassembly of the signal will be required.  You will need to be very careful of the three leads going up the pole to the lamps. Use a meter or jumpers to see if a high resistance joint or open resistor is the problem.