At the last job I had before retiring from working for others, we filled out excel timesheets on the computer. Vacation, sick time, etc had their own activity codes. The total for each week had to add up to 40 (or more for salary types) and the timesheets were submitted, either electronically or hard copy every pay period. The accountant extracted the numbers and they all appeared on the paycheck stubs. This worked fine for the company, which had about 45 employees and one accountant. It was fairly elaborate because the company did about 300-400 projects per year, some lump sum, some hourly, etc, so the project time had to be accounted for in fair detail, along with personal time.
I've thought this over a little and think I probably would have everybody fill out excel timesheets and submit them electronically. It would not be difficult to have another excel spreadsheet for my use only that processed the information, adding accumulated sick/vacation time, subtracting used sick/vacation time, sorting the hours spent on the different project numbers, and preparing invoices. Being an engineer, I might do this in Mathcad instead because it has more powerful programming and document preparation features.
I hope this helps.