I'd like to address some other things that may become an issue with your rig...
Since you do not have an FX loop, I'm assuming that you are putting your timefactor before your amp and using the amp for your overdrive sounds.
Placing the delay before the overdrive will compress the delays in an unpleasant way. If you do not have an FX loop and need to put your delay before an overdriven amp, I would suggest setting the amp clean and using an external preamp or overdrive pedals (Marshall, line6, radial, etc) for your overdrive sounds and place your timefactor, and other time-based FX like chorus, flange and reverb, between the overdrive pedals/ preamps and amplifier input.
Now that being said, you might like your timefactor before your amp, so don't let me judge you!
Now, back to your Timefactor and allowing trails when you bypass it...(info in the manual)
There are two ways to do this...
you need to set the timefactor for DSP+DLY Bypass mode....(info in the manual)
Since in this mode, your guitar is going through a digital converter in the timefactor, your guitar tone might be affected... So, I would recommend placing the timefactor into a gcx loop when you are not using the delay. To get trails, the gcx loop must be active before and after your preset switch.
You must also send a midi cc from your midi foot controller to bypass the timefactor with the GCX loop active all of the time .... unless you are not using the delay and then you can bypass it using one of the gcx FX loops.
another way to connect the timefactor to provide trails without affecting your guitar tone is to do the following...this will be a parallel FX setup and will require a mixer as additional equipment.
Assuming that you have 4 other pedals that will go in front of the amp (this will include any overdrive pedals connected before the timefactor as I mentioned before)
1. connect your guitar to the gcx loop 1 IN and loop gcx loop 2, 3, and 4. Insert your distortion, fuzz, overdrive and compressor pedals in the GCX loops 1 to 4.
2. Then connect the output of gcx loop 4 to the GCX Front panel GUITAR IN. This will allow you to split you overdriven guitar signal using the gcx buffer and the guitar out and feedthrough jacks on the gcx rear panel. Then we will send 1/2 of this split signal to an external mixer and the other 1/2 to the timefactor input, (through another GCX loop), to set-up the parallel FX configuration as follows...
3. Connect the GCX Rear Panel GUITAR OUT out to channel 1 of an external line mixer. (you can use a rack-mounted one) this will be your dry guitar sound that will never go through the digital converter of the timefactor, therefore your 'tone' will never get messed up.
4. connect the GCX rear panel feedthrough jack to the INPUT of gcx loop 5
5. connect the SEND of gcx loop 5 to the input of your timefactor. (since you already have a dry guitar signal going to the mixer, make sure that your timefactor patches are set with the MIX at 100% FX and no dry signal) The timefactor will be active when gcx loop is active.
6. connect the output of the timefactor to channel 2 of the external line mixer
7. when you de-activate loop 5, the input to the timefactor will be cut allowing your delay trails to be mixed with your dry guitar sound in the mixer. With this set-up, It doesn't matter which bypass-mode the timefactor is set to.
8. the output of the mixer can feed other gcx loops with other time-based FX connected, (flange, chorus, reverb, etc), or you can connect the output of the mixer directly to your amplifier input.
As stated before, the amp should be set clean. (your overdrive sounds will be produced by preamps or pedals before the amp.)
You can set the relative dry and FX levels at the mixer.
you'll have get a line mixer and experiment with all of these connections so that you can hear the benefits.