Database login response time

Is there any way to capture login response time using sqlplus. our database login sometimes takes more than 2 minutes so would like to setup a monitoring script.

Have tried this but its not working

C:\Users\aangusamy>sqlplus /nolog

SQL*Plus: Release 19.0.0.0.0 - Production on Sun Oct 2 12:34:19 2022
Version 19.3.0.0.0

Copyright (c) 1982, 2019, Oracle. All rights reserved.

SQL> set timing on;
SQL> conn TEST/XXX@TEST
Connected.
SQL> select * from TEST;

DBNAME  
--------
TEST

Elapsed: 00:00:00.03
SQL>

It shows the elapsed time for query but not for login.