DS1302 as a counter/count-up timer
Do you mean only accumulate during powered/driving, or also during standing still? 

If the former, just get the start time in setup, then in loop continuously get the time and calculate the difference between it and the time read in setup. Since you don't know when power is lost you need to continually write the elapsed time to some form of non-volatile memory. You could use the Arduinos EEPROM, but that can wear out over time. It's better the use the DS1302s 31 byte of battery backed RAM. Next time the arduino starts up you need to read out this value and add this to the difference. 

In case of the latter, you can halt the DS1302 so it stops incrementing time.