Fork trail vs chainstay length in steering Is fork trail or chainstay length is a bigger determinant in the overall steering of the bike?

Consider an arbitrary frame that I think is steers too slowly.  I'm going to rebuild it because I want a fun project, have some scrap metal, all the parts, and I want to build another similar bike that steers a bit quicker and is more racy.

All other things being equal, mainly the head tube angle, would building another frame with shorter chainstays be a better way to go about it than using a fork with less trail?

I'm interested in the rate of change in the steering of the bike while changing those two factors, and which one affects the steering more, and by how much if it can be measured - i.e. 1mm change in trail could be offset by 2mm change in chainstay length (that's probably wildly inaccurate - I'm hoping to hear from some frame builders).
Because you steer a bicycle with the front wheel (and weight offsets), the steering of a bicycle is almost entirely determined by the geometric parameters of the front wheel and where it is located. The most determining factors are:


Trail
Wheel flop factor
Front wheel radius


Trail and wheel flop factor are determined by steering angle, fork offset and wheel radius.

The chainstay length is irrelevant in this respect, but it does matter for the overall handling of a bicycle. For example it has an influence on how well a mountain bike climbs. For road bikes it has some influence on the weight distribution between both wheels.

There are tandems which handle like a good road bike (except for the turning radius). They essentially have "chainstays" that are almost 1.5 m long.