A digital input should require eff all current so volt drop shouldn't be an issue. Given the completely fucking nerd nature of my day job I once built a timing setup for my old pump track that ran off a spare PLC I had and used FreeSCADA to display a timing board on a laptop with the last 4 lap times.Here's your overkill method. https://farmtek.net/motor_sports.html
The more DIY option requires 2 used inner tubes, 2 pressure switches, some zip ties, a shitload of speaker wire and an arduino, maybe some resistors to make a whetstone bridge so you can run the sensor further from the Arduino at a higher voltage since the wire is going to have a good amount of voltage drop. You cut the inner tubes, fold over and zip tie one end so its sealed, zip tie the other end over the pressure switch, fill it with enough air that when a bike tire runs over the tube it trips the switch (like how the bells at ol' timy gas stations worked). String those across the start and finish lines, and write a simple timer program in the Arduino, make sure you have it ignore the input for each tube for a couple seconds after it gets the first input to not count both tires as separate riders.
Given the nature and length of Enduro stages it would be hard work to intercable the start and finish. A timestamp over radio signal would cost more but freaking hell it would be worth it.
Whats Freelap going for these days? Is there a cheaper knock off yet?