Last week I thought about this when my solder paste dried and was hard as hell to squeeze out!
This seems a nice motor. Encoder output, fine thread, high reduction ratio and fits inside the syringe!
https://www.aliexpress.com/item/1005001785275240.htmlI don't think I'll use a 18650 heavy monster there. Maybe something small like 10180 or 14250.
I was making some calcs. Given the 16mm plunger (201mm²), the motor has 0.35mm thread, 240 reduction ratio.
For each complete rpm, the syringe would pull out 0.35*201 = 70mm³ of paste.
The average 0805 pad size is 1.3*0.7m= ~1mm². Let's say you put 0.5mm height of paste, it would be ~0.5mm³ of paste.
0.5/70=0.07rpm required.
With 240 reduction = 1.71 motor turns.
I don't know the resolution of the encoder, but it seems it will require a really fine control. Plus retraction to avoid spilling.