Probing a waveform with features that have orders of magnitude difference in times
The pulse jitter shouldn't be a problem. Set your time base to 200ns (500ns if the jitter is high) and set display mode to infinite persistence. You should get all your pulses on top of each other, and be able to measure minimum and maximum pulse width.  

The pause jitter is a different story, and I'm not sure the TDS3034 can handle a 2s trigger delay when your time base is for instance 1\$\mu\$s. This may call for a logic analyzer, which has a lot more triggering options. You may be able to set a trigger delay to 1 999 998\$\mu\$s. You won't see the exact waveform, i.e. voltage levels, but for measuring jitter this will probably not be important.