Maybe the JunTek can be made to do this. RTFM and use Google. I suspect it can't.
My experience of this was with a FeelTech FY6800 (also sold under several other brands). It has a sweep function but no sync or gate output. This was something I found very irritating as one of the reasons I bought it was to use it as a sweep generator. It does have a VCO input. It has the peculiar sync output for synchronising other units.
I found two ways of making it produce a synchronised sweep. I set up a five step staircase sweep, and made it slow enough that a frequency meter would have long enough to determine which frequency it was at, at each step.
Use Channel 2 to produce a sweep voltage for the VCO and connect the Channel 2 output to the VCO with a BNC cable. This can be done, but the VCO isn't completely linear and you can't assume the start and end frequencies are what you would like then to be. It involves a specially set up sweep. Possible but painful and the sweep might have to be different for different ranges. If you are using it to check scope Y amps, you may not care if the sweep starts at 20kHz or 50kHz and ends at 19.5MHz or 20.5MHz. Maybe the Juntek doesn't have the problem with the VCO.
Use Channel 2 to produce a sweep, the amplitude doesn't matter much, and use that to FM modulate Channel 1 using the parameter set up for Channel 1 modulation. Trigger the scope on the falling edge of the sweep from Channel 2. I found that worked very well and was convenient. You could also set up a scope in X-Y mode and use the sweep directly.
Since then I've bought a Siglent function generator, and that has properly implemented sweep function with a sync output for the sweep. It works as expected with no messing about, but it's about twice the price of the Juntek.