I don't know exactly what toolbar you're talking about, but it's possible to add a menu command to Tampermonkey's action menu.
Since your script should be able to run at any page you need to @include all pages what might slow down pages with a lot of iframes a little bit.
This script will execute the main function (with the alert statement) only if the menu command was clicked.
// ==UserScript==
// @name Run only on click
// @namespace http://tampermonkey.net/
// @version 0.1
// @description Run only on click
// @include /https?:\/\/*/
// @copyright 2012+, You
// @grant unsafeWindow
// @grant GM_registerMenuCommand
// ==/UserScript==
GM_registerMenuCommand('Run this now', function() {
alert("Put script's main function here");
}, 'r');
Accessing the pages functions is possible by two ways:
function main () {
window.function_at_the_page();
}
var script = document.createElement('script');
script.appendChild(document.createTextNode('('+ main +')();'));
(document.body || document.head || document.documentElement).appendChild(script);
or just:
unsafeWindow.function_at_the_page();