* Broken or damaged shift linkage: This is the most common and often easily repairable cause. The linkage connects the shifter to the transmission; if it's broken or misaligned, you won't be able to select reverse.
* Internal transmission problem: Something inside the transmission itself could be broken, like a broken reverse gear, a stripped shift fork, or other internal damage. This is a much more serious and expensive repair.
* Incorrect adjustment: While less likely, the clutch adjustment could be significantly off, preventing reverse from engaging.
If your S-10's manual transmission lacks reverse, it needs professional diagnosis and repair. Don't attempt to drive it extensively, as further damage is possible.