Rather than using mboxDefine/mboxUpdate I'd recommend you use the adobe.target.trackEvent function (only works for at.js). Tanvi linked to a help doc with some details on it. Here is a simple sample though:
You can pass the parameter as a "profile.param1" if you want it to be sticky for the visitor. However, in your use case where you have a profile script looking for attribute you probably don't need to use the "profile." because the profile scripts are sticky too.