This may interest the people who own a Uni-T UT71 meter.
As you would have noticed, the normal continuity test is latched, but rather slow on these meters.
I found a way to achieve a fast latched continuity test which doesn't involve any modifications.
1. Turn the range switch to Ohm and select the diode mode by pressing the blue button twice. You are now in the 4V range.
2. Press the RANGE/SETUP button until the meter beeps and displays OFF in the 'low' setting.
3. Press the HOLD button once to access the count display.
4. press the HOLD button repeatedly to select each number in turn.
5. Change each number with the + and - buttons until your display reads 27600 and press EXIT to store it.
6. You are now in a fast mode for your continuity testing, staying in the diode range.
7. When you are done with the continuity testing, press RANGE/SETUP until it beeps again, then press STORE to display OFF in the low mode.
8. Press EXIT to return the meter to its usual state.
It is a bit of a convoluted procedure, but at least the function is available if you don't have another meter at hand.
Happy testing!