Q: What is the field "historySize" on the GUITextInputBox for?
The field controls the number of messages that can be up/down arrowed through.
The scroll history in the box is already tracked and handled internally, so as long as the up and down arrow keys have not been overtaken by script, then while the cursor is in the text input box, pressing the UP arrow will cycle through previous entries, and you can go forward through the entries with the down arrow.
A history size of 10 will store the last 10 values that were entired. Hitting ENTER will clear the text box and add the value to the history. A historySize of 0 will prevent the textbox from automatically clearing when ENTER is pressed.