+6V to -6V is 12Vpp, but also specifies that the expected modulation signal must not have DC offset. Thats something else to check. 0V - 12V would also be 12Vpp but violate the given constraint.
I can not now test using SDG2kX.
But this is how it is with SDS1kX and for Ext modulation specs are same if look both datasheets.
External modulation is DC coupled. Signal nominal/typical range is +6V to -6V and input impedance is 10kThese are typical values. (limits are min 11Vpp and max 13Vpp for full 100% mod depth)
Maximum modulation frequency is 50kHz
Modulation input is Aux In/Out BNC in rear panel, later I use ExtMod name for it.
Modulated signal output voltage level is roughly 0 when ExtMod input is -6V
Modulated signal output voltage level is "full" when ExtMod input is +6V
When signal to ExtMod input is 0V modulated signal level is half way from max.
If it works or not it can test just using suitable DC and oscilloscope.
SDG1000X: (apparently the SDG2000X works in the same way in this particular case - least I believe)
Very first set SDG for factory defaults.
Set SDG output for Hi-Z and connect it to iscilloscope 1Mohm input.
Set SDG for example 1MHz sinewave 1Vpp
Turn modulation ON, Type AM and Source External.
Adjust ExtMod DC voltage to 0V (BNC center to 0V or just do not connect anything to ExtMod so its level is around 0V)
Oscilloscope should now display around 1Vpp signal.
Next
Adjust ExtMod DC voltage to +6.0V (BNC center to +6V BNC GND is GND aka 0)
Now oscilloscope should display around 2Vpp signal. (with 3V around 1.5pp)
Adjust ExtMod DC voltage to -6.0V (BNC center to -6V BNC GND is GND aka 0)
Now oscilloscope should display around 0Vpp signal. (with -3V around 0.5V)
Most simple "go/no go" style test can do using just onew battery.
Also of course SDG other output can use as adjustable voltage source also for playing this...just connect it using coaxial to rear panel ExtMod only remember adjust this channel for HiZ Load (or 10kohm load) because ExtMod impedance is 10k. If adjust it for HiZ level error is irrelevant in this case.
If you have now example -6V to +6V 1kHz sinewave signal you have then 1MHz signal AM modulated with 1kHz and modulation depth 100%.
Note that ExtMod input true levels/mod depths may have some differeences between individual units and manufacturing lots.
If it do not at all works like this, then there is some problem on your cables or other things OR SDG ExtMod is broken.