The sequence where Simon maps the caves and find the SM-8 starts at about 00:57:24. The SM-13's coordinates at the start are 702.07, 652.77. He's relying pretty heavily on the camera at the start, his process being: take a picture, mark his surroundings on the map, rotate the rover's direction by 90°, repeat.
Above is the condition of the map at 00:58:25 (hi Ellie), right at the start of Simon's mapping endeavors. At 00:59:35, we cut to Simon glaring at the aggressively taped down camera shutter as the tape slowly peels off.
(side note: Simon's stuck using medical tape, my guess is a micropore paper surgical tape, which 1. is intended to stick to skin/gauze/porous surfaces, not metal, and 2. doesn't even stick to its intended surfaces very well in my experience. Somebody please get Simon some duct tape.)
Based on how much used tape is seen lying on the floor at 01:00:35, this is just the most recent of many attempts to keep the camera going while he navigates and charts the caves.
This seems to have been a decently effective method, as we get a glimpse of the map at 01:00:13, and Simon's made significant progress in charting the caves:
My best guess as to what happens off screen leading up to 00:59:35 is as follows:
Simon tapes down the camera shutter and starts to navigate based on the resulting pictures, periodically getting up to take notes of his surroundings on the map. The constant stream of pictures also allows him to an eye out for any hazards (like Ellie). He makes significant progress with this method, but it has its drawbacks.
The tape doesn't last long, so Simon is constantly having to get up and either re-adhere or add more tape to the camera shutter to keep it going.
He gets increasingly frustrated with the limited time the shutter will stay taped down, building up to the interaction seen at 00:59:35, where Simon has layered tape over the button and is nervously watching it slowly betray him.
Having run out of tape, Simon abandons the camera and instead relies on the proximity sensor, leaving himself unaware of threats such as sudden drops, wildlife encounters, etc.