Here's a working solution, taking mkopriva's advice:
When executing a template, pass some custom parameter with dummy data. Here, I just create a "PageHome" parameter to pass to the template, and value is a simple "1", but it could be any value:
tmplHome.ExecuteTemplate(w, "base", map[string]interface{}{"PageHome": "1", "Data": events, "UserFirstName": &u.FirstName, "UserProfilePic": &u.ProfilePic})
Then, inside the template itself, a simple if statement to check if the parameter exists, and do something accordingly:
{{ if .PageHome }}
<body class="PageHome">
{{ else }}
<body>
{{ end }}
All my other template executions don't pass a "PageHome" parameter at all, so the if statement never passes as true for them.
There's probably a more advanced solution using a functions via a template function map, and having a consistent "PageType":"something" parameter in all template executions, but in the end you still have to define a parameter per template execution and still have to build up if statements in your templates anyways.