Just for fun,I decided to play around with the Tek 7613 to see if I could see signals at around the rate the OP was probing.
As I don't have anything which will produce pulses at such a low frequency,I tried just touching the probe & ground lead across a "C" cell,with the 'scope set to 500mS/div & dc coupled.
To my surprise,I saw no vertical deflection,just the spot doggedly scanning across the screen.
I changed to a faster timebase setting---still no sign of the dc shift expected,but lots of 50Hz hum.
It took a bit of fiddling before I hit the "Duhh!" moment.
An open circuit ground lead!
Fixed that,& had another try.
As I anticipated,the normal display didn't show much,but the "storage" mode did--for a while,before I stuffed it up trying to make it better!
Anyhow,all you would see would be a bit of a thickening of the trace if there was external grot on it-----none here at all.
I bet it would have picked up any HF stuff around,along with the 50Hz,if the probe's ground lead was still faulty,though.
Maybe the OP should check the continuity of his ground lead,just in case!