I was never able to pass a new field to the query using a separate token. Splunk was always waiting for data input. I solved the issue by using the radio button's statement to add the field (Logon_ID).
<input type="radio" searchWhenChanged="true" token="priv_login_tok">
<label>Login Status</label>
<choice value="4624 Logon_ID!=0x0">Successful</choice>
<choice value="4625">Failed</choice>
<initialValue>4624</initialValue>
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