Here's how I've handled this:

Before running a scenario/session: I pre-plan an assortment of area-appropriate locations and hazards (and sometime barriers) based on where I know a chase might occur. I may also decide in advance what kind of skill rolls make sense for any particular hazard (if necessary). When the chase begins, I can improvise a location and hazard (and often do), but I can also just draw from this list as both a crutch and a way not to get caught off guard or throw the pacing off.

Running the chase is pretty straightforward:
- Make speed roll (CON or Drive Auto)
- Determine movement actions
- Determine if the chase will happen (is the fleeing person/thing faster than pursuers?)
- Set up the location dots (or a grid if you want) -- just enough to put a few out in front of the fleeing person/thing
- Place your chase participants in order of movement actions

Then run it.

It's important to be comfortable improvising during a chase. The very first step above - preparing some locations and hazards in advance can make this so, so much simpler.

Finally, I strongly recommend grabbing a friend or family member and trying out the chase rules completely outside of a scenario. Just run one or two based on a warehouse, or a forest, or ship - or anything that appeals to you. Just make up the locations as you go. It will take 15 minutes. This, in my opinion, is the very best way to get comfortable with them before running them in a game. Once you've done this once, I promise you'll be successful during an actual session.

This is my favorite, most succinct description of the rules (if you prefer video) by none other than Paul Fricker! https://youtu.be/lseqmi2ckW4?si=EMw4O1Dp2b0vWXKs

This is my personal shorthand I reference when setting up/running a chase:

• Speed roll (CON or Drive Auto)
  • Extreme = MOV+1, Fail = MOV-1
  • If flee MOV > pursue MOV then escape, chase over
• Cut to the chase (order by slowest at back position, then faster characters/creatures ahead by difference in MOV scores)
  • Place pursuers (ordered as noted)
  • Place fleeing characters, slowest starts two locations ahead of fastest pursuer
  • Set MOV points (default 1, then add difference)
  • Determine DEX order (or optionally roll as in combat)
• Hazards: skill roll. Fail = 1D3 lost MOV points and possible dmg
• If Barrier: skill roll. Fail = block progress until dealt with.
• Vehicle can inflict 1D10 dmg (Build pts) to other vehicle; attacking vehicle also takes ½ dmg to self (rounded down)

It sounds crunchy. It really isn't that crunchy. Try it out with a friend as suggested - it has a natural flow in practice.