Above are links to your specific product that you may find handy.
The Tork DTS400B is a 4 channel timer
4-channel means you can control 4 separate loads, and each load can have a different timing schedule
Each channel or Load is wired separately.
To bypass the timer to check the sign, we can do that with the wiring
Open the wiring PDF above.
There are 2 boards of screws.
Wires to the clock are on Lower board and to the left.
These wires operate the timer clock only and we will not work with them.
The Loads (your sign) are wired to the other terminals on Lower and Upper board.
Below is a graphic taken from wiring PDF.
It shows a close up of the Lower board where your Loads connect.
I added Load1 and Load2 to the graphic so it is easier to talk about the terminals.
Before moving any wire, mark the wires with tape and numbers so there is no confusion later when you want to put the wires back.
Take a digital photo of the marked wires before any wires are moved.
To bypass Load1 timer functions, move the N wire to the same terminal as the L wire.
This will close the circuit, so the Load will be ON continually.
To bypass Load2, move the N wire to same terminal as L wire.
In this way, you can check each of the 4 possible Loads separately.
When finished checking the Loads, move your wires back.
Also above, I included the programming PDF so you have a digital (and search-able) manual for the programming functions.
Add a comment if you need more help.