How can I check that the GPS receiver is sending data to the transponder?
Your puck (GlobalSat BR355) runs on 5v and the UART line idles high (it is pulled high when there is no traffic).   The first thing you need to do is find the power lines that go to the gps puck -- connect wires to these lines (5v and gnd) and run them to the spot where you want the button/led.   Then make this circuit:



The value for R1 should be 150 ohms (which will yield under 20ma of current through the LED, assuming your led has a voltage drop of 2.1v (which the ones in the link I provided do have))



Here is a link to a transistor that will work for Q1:

https://www.digikey.com/product-detail/en/central-semiconductor-corp/2N4403/2N4403CS-ND/4806893

Here is a resistor that will work for R1:

https://www.digikey.com/product-detail/en/stackpole-electronics-inc/CF14JT150R/CF14JT150RCT-ND/1830603

And here is a link to a selection of LEDs you can use (all with voltage drop of 2.1v; Any of these should work; just choose a color and form factor that works for your application):

https://www.digikey.com/products/en/optoelectronics/led-indication-discrete/105?k=led&amp;k=&amp;pkeyword=led&amp;pv16=2&amp;FV=1140050%2C4fc0015%2C1f140000%2Cffe00069%2C87c001d&amp;mnonly=0&amp;ColumnSort=0&amp;page=1&amp;quantity=0&amp;ptm=0&amp;fid=0&amp;pageSize=25

Here is a link to a selection of pushbuttons that should work -- just choose a form factor you like (look at the datasheet for the ones with 4 pins -- these are just two pairs of pins (each pair is connected) for mounting ease -- two pins can be harder to mount on a circuit board):

https://www.digikey.com/products/en/switches/pushbutton-switches/199?k=pushbutton&amp;k=&amp;pkeyword=pushbutton&amp;pv130=7&amp;FV=1140050%2C2dc0017%2C3ac000e%2C1f140000%2Cffe000c7&amp;mnonly=0&amp;ColumnSort=0&amp;page=1&amp;quantity=0&amp;ptm=0&amp;fid=0&amp;pageSize=25



I personally recommend you use something like this for the button:

https://www.digikey.com/product-detail/en/e-switch/KS-01Q-01/EG4791-ND/2116270

For this button here is a picture and a schematic (as you can see, the pins on either side of the flat side of the button are connected:





And something like this for the led:

https://www.digikey.com/product-detail/en/cree-inc/C503B-RAN-CZ0C0AA1/C503B-RAN-CZ0C0AA1-ND/6561758



Just wire these components up according to the picture and solder them together -- I'll leave how to mount the switch and the LED up to you but make sure once you are done you cover all the exposed wire with glue and/or electrical tape and/or liquid electrical tape so they don't accidentally short out.   Also make sure no exposed wires within the circuit are touching where they shouldn't touch (especially make sure you separate the pins of the transistor because if they accidentally touch the circuit will not work and you may damage your gps receiver -- long story short be careful in your wiring and make sure nothing is touching that shouldn't.