Python + Mechanize - Emulate Javascript button click using POST?

I'm trying to automate filling a car insurance quote form on a site: (following the same format as the site URL lets call it: "https://secure.examplesite.com/css/car/step1#noBack")

I'm stuck on the rego section as once the rego has been added, a button needs to be clicked to perform the search and it seems this is heavy Javascript and I know mechanizer can't handle this. I'm not versed in JavaScript, but I can see that when clicking the button a POST request is made to this URL: ("https://secure.examplesite.com/css/car/step1/searchVehicleByRegNo") Please see image also.

How can I emulate this POST request in Mechanize to run the javascript? So I can see the response / interact with the response? Or is this not possible? Can I consider bs4/requests/robobrowser instead. I'm only ~4 months into learning! Thanks

# Mechanize test
import mechanize

br = mechanize.Browser()
br.set_handle_robots(False)   # ignore robots
br.set_handle_refresh(False)  # can sometimes hang without this
res = br.open("https://secure.examplesite.com/css/car/step1#noBack")

br.select_form(id = "quoteCollectForm")
br.set_all_readonly(False)    # allow everything to be written to

controlDict = {}

# List all form controls
for control in br.form.controls:
    controlDict[control.name] = control.value
    print("type = %s, name = %s, value = %s" %(control.type, control.name, control.value))

# Enter Rego etc "example"
br.form["vehicle.searchRegNo"] = "example"

# Now for control name = vehicle.searchRegNo, value = example

# BUT Now how do I click the button?? Simulate POST? The post url is formatted like:
# https://secure.examplesite.com/css/car/step1/searchVehicleByRegNo

Javascript POST