The tab bar and its contained tabs can be read by AppleScript using System Events and UI-Scripting. Something like this:
tell application "System Events"
tell application process "Google Chrome"
tell (first window whose subrole is "AXStandardWindow")
tell group 1
tell group 1
tell group 1
tell group 1
tell tab group 1
return {position, size}
end tell
end tell
end tell
end tell
end tell
end tell
end tell
end tell
And yes – you can get the position and size of the buttons as well.
An alternative could be a gesture trigger. Short movement with the mouse to the right while pressing cmd (with a modifier it is safer) The mouse can be anywhere.