What body fluid is most likely to expose the EMT to HIV?

Blood.

Other fluids also carry HIV, but in trace amounts. Saliva will not freely spread HIV. (I've heard that you could drink two gallons [four liters] of saliva from an infected individual and still have just a small percentage of risk.) Sweat is even less potent. This is why universal precautions (i.e. gloves) are a must for every single run you go on. It only takes a drop of blood to land on or near a break in your skin for you to run the risk of infection.