Problem when running ['node_modules/.bin/cap', 'sync']

[pinpontitit]

Hi,
I am not quite sure that capacitor is in cause here.
So instead of opening a bug issue I prefer to discuss here my problem, hoping that someone could lead me to the real cause.

I am working on Windows.
npm is installed. gulp is installed globally. Capacitor also.
npx cap sync and npx cap init were runned.

I'm trying to debug an android app which uses a gulpfile.js.
The gulpfile.js, in the app repository, is pointing to 'node_modules/.bin/cap'

And, everytime I run gulp, it ends with an error relating to "android":

[01:30:42] 'android' errored after 206 ms
[01:30:42] Error: Command failed with exit code 1: node node_modules/.bin/cap sync
C:\Users\Tombouctou\floccus\node_modules\.bin\cap:2
basedir=$(dirname "$(echo "$0" | sed -e 's,\\,/,g')")
          ^^^^^^^

SyntaxError: missing ) after argument list

I tried editing the cap binary, with legacy code (backticks). It solves this parenthesis issue, but after I have another issue:
Unexpected token "case".
If I fix that I have again another issue anywhere else on the same file, and so on....

The developer of the app I'm trying to debug, says that it's because I am on Windows but he don't know how to rewrite this line on the gulpfile.js :
const {stdout} = await execa('node', ['node_modules/.bin/cap', 'sync'])

I don't know either.

Do you reckon I should point this line to somewhere else ?
Or do you think I should edit the .bin/cap file and change the code inside, which is :

basedir=$(dirname "$(echo "$0" | sed -e 's,\\,/,g')")

case `uname` in
    *CYGWIN*|*MINGW*|*MSYS*) basedir=`cygpath -w "$basedir"`;;
esac

if [ -x "$basedir/node" ]; then
  "$basedir/node"  "$basedir/../@capacitor/cli/bin/capacitor" "$@"
  ret=$?
else 
  node  "$basedir/../@capacitor/cli/bin/capacitor" "$@"
  ret=$?
fi
exit $ret

I'm totally lost.

Thanks