Ok, self answering my question 
I have just put the values into the parameter which I can access then in my method
changeTemplateBasedOnType
New method definition is now:
Code:
<tpl for="."> {[this.changeTemplateBasedOnType(showAssignForType, values)]}
</tpl>
And getting the values into the view:
Code:
changeTemplateBasedOnType: function(type, values) {
var returnString = null;
if(type==='person') {
returnString =
'<div class="detail_container">' +
'<div class="pers_det_image"> <img src="' + values.IMGURL + '" width="200px" height="200px" /></div>' +
'<div class="person_text_container">' +
'<div class="pers_det_name">' + values.NAME + '</div>' +
'<div class="pers_det_lastname">' + values.LASTNAME + '</div>' +
'<div class="spacer"></div>' +
'<div class="pers_det_bd">' + values.BIRTHDATE + '</div>' +
'<div class="spacer"></div>' +
'<div class="pers_det_street">' + values.STREET + '</div>' +
'<div class="pers_det_zip">' + values.ZIP + '</div>' +
'<div class="pers_det_country">' + values.COUNTRY + '</div>' +
'<div class="spacer"></div>' +
'<div class="pers_det_tel">' + values.TEL + '</div>' +
'<div class="pers_det_notes">' + values.NOTES + '</div>' +
'</div>' +
'</div>';
return returnString;
}
else if(type==='object') {
returnString =
'<div>' + values.TITLE + '</div>' +
'<div>' + values.GUID + '</div>' +
'<div>' + values.ALT_ID + '</div>' +
'<div>' + values.BASE_CAT + '</div>' +
'<div>' + values.MISSING + '</div>' +
'<div>' + values.NOTES + '</div>';
return returnString;
}
}