How would you measure the rate of this SN1 reaction?
If you want to measure it with an electronic device I would recommend some spectroscopic technique such as IR, Raman, 1H-NMR etc. or using a digital pH meter. For the spectroscopic techniques you should probably cool down the solution to minimize error during the measurement or alkalify it to avoid further reaction.
However if you want to avoid these methods and you have enough soultion-volume you could try titrating it with NaOH solution and a proper indicator.