If your HPI mini indeed has one output, you have all sorts of problems.
You will need a center tap on your coil windings.
Ill say this up front, I am bad at nomenclature and am not an EE, but I have made my own ignitions and lighting coils from nothing but a spool of magnet wire and a stator frame and used reg/recs of whatever I had on hand, but not all are created equal and not all will work 100%
So looking at what you have you have the "Bridge Rectified" trailtech Reg/Rec
It is looking for 2 AC output wires, one is the full path, IE it runs through all the coils and down to earth, the other one is a half tap, it goes about half way and pulls AC from there.
For a crude explanation of why you need this from my unschooled brain. is creates a phase shift or -ve of the AC wave, which from my understanding for full bridge rectification you need.
Your mini has one AC output wire, the single yellow, so you don't have that phase shift. so the rectifier is not operating as normal.
You can add in your own half tap, or "float the ground" and pull the ground off the frame of the stator, solder a wire to it and run it to the secondary ac input on your rectifier. Personally since it has 3 coils for lights I would just find a spot on the magnet wire in between coil 1-2 or 2-3 and just scrape back the coating and add in a wire and hot glue or silicone it to keep it secure and leave the ground on the last coil. As long as you don't cut the wire its easy enough to just pull it off at a later date and not wreck your stator.
This is the way like 90% of every single phase OEM modern day lighting stator works.
And I am ok if someone comes in and tells me I butchered that explanation.
I have photos and wiring diagrams of what I am explaining somewhere but I will have to hunt for them.