Set on "Auto", the o'scope uses the channel 1 input as its "trigger" (I think).
Which scope do you have? For most scopes "Auto" refers to automatic trigger 'level', not trigger source.
You're not likely to ever need the EXT trig if all you ever look at is sine, triangle, or square waves. All those signals are repetitious and easily triggerable using the vertical input as a trigger source.
Here's the setup I always use when using a sine wave sig gen, scope, and amp. Put a Tee connector on the sig gen output. Connect one cable between the Tee and scope channel 1. Trigger the scope on channel 1. Connect another cable between the Tee and the amp input (or injection point). Doing this allows you to always see your input signal. Comes in handy if you want to change signal level or frequency.
Now connect your scope probe to scope channel 2. Set the vertical mode to "alternate". Now you can see your input signal and the signal with the probe as you examine different points along the amps signal path. You readily see the gain, loss, phase shift, distortion, etc., and can quickly compare to the input signal. Since you're triggering on the input signal on channel 1, you don't have to readjust trigger levels as you move the probe around. (I know that using "Auto" triggering usually means you don't have to be readjusting trigger levels, but in my line of work I often need to have complete control over trigger levels and slope, so I mostly use "Normal" triggering and diddle the level and slope as needed)
I have a couple sig gens, one has a sync output, the other does not. When I use the sig gen with the sync output, I connect that sync output to the scope EXT TRIG input, select EXT TRIG source, NORMAL TRIG mode, and use the manual trig level. My sig gen sync output is a constant level (ie, does not change with sig gen output attenuator) square wave that's ideal for scope triggering.
While I'm at it, does Kobican make good cables? (specifically part #172-2129-EX)
I'm not familiar with that brand, but I would not be too concerned about BNC cable quality for guitar amp work, unless they look really cheezy! I would recommend getting 6 each 6' BNC cables, 2 each probes 1X and 10X, and a double handful of various adapters, TEEs, barrels, etc.