What kind of phone do you have? Why not use the default apps on the phone such as the built-in stop watch, notes and screenshot features, assuming you have a smartphone.
Personally, I just screenshot my home screen on my iPhone that shows the clock app. You'll notice it shows down to the second. I think it's useful because you can carefully "screenshot" all the timing points you need, note which screenshot is what and then you can reference all this when you're ready to do your report. If you're adamant on using digital timings only, just use the the built-in stop watch on your phone, then screenshot it if you have multiple timing points you need to account for, for your shop.
Shopping the Greater Denver Area, Colorado Springs and in-between in Colorado. 33 year old male and willing to travel!