I have 6 outlets that do not work.

However, I can provide guidance on using a basic voltage tester to check for live wires when troubleshooting a light fixture installation.
Using a Voltage Tester:
Non-Contact Voltage Tester:
If you have a non-contact voltage tester, it's a handy tool for quickly identifying live wires without direct contact. Hold the tester close to the wire insulation or the terminal screws, and it should indicate the presence of voltage without making physical contact.
Contact Voltage Tester:
If you have a contact voltage tester, make sure it's designed for the voltage level you're working with (e.g., 120V for residential electrical systems).
Turn off the strength to the circuit on the circuit breaker or fuse box.
Safety First:
Always prioritize safety. Make sure the power is turned off before working on any electrical components.
Test the Tester:
Test the voltage tester on a known live circuit to ensure it's functioning properly.
Check the Wiring:
Once confirmed, turn off the power to the circuit you are working on.
Use the voltage tester to check each wire connected to the light fixture. Verify that there is voltage on the wires.
Neutral and Hot Wires:
Typically, a light fixture will have a hot wire (usually black) and a neutral wire (usually white). Make positive each wires are linked properly.
Ground Wire:
Check for a ground wire and ensure it's properly connected. Some light fixtures may have a green or bare copper wire for grounding.
Switch Position:
Ensure that the wall switch controlling the light fixture is in the ON position.
Bulb Check:
Confirm that the light bulbs in the fixture are working and properly installed.
Circuit Breaker Check:
Double-check the circuit breaker or fuse for the lighting circuit to make sure it hasn't tripped or blown.

From what you are stating I am going to make a few assumptions. That the new switch has been connected properly and that the lamp you are supplying works OK in a different outlet. The only thing left to do is to make sure that you have voltage on the switch. Once this has been ascertained, if no voltage, then you have a broken connection or wire on one of your other switches or outlets as the power is simply 'jumped' (in parallel) around the house from switch to switch or outlet to outlet. If the switch has power, make sure that it is indeed going through the switch when activated. If it is, then the break is between the switch and the outlet. A cheap non contact 'voltage stick', which is a tester which has audible and visual indication when it comes near voltage is a good tool to have if not adept with electrics. Please be careful. Cheers Bob

Any 303 or 357 silver oxide battery will work. You can find these at battery outlets, box stores, and watch repair stores.

The 504A uses two silver oxide 357 button batteries. The black top is just press fit in. Gently pry it off. The batteries install with the positive side down.

Model number is not known.
I did not know that Kitchler transformers have a circuit breaker.
Usually they have an override switch.
Did you set the timer to override, what does your product manual say?
Is the transformer humming? Kitchler transformer are supposedly non-audible, but there should be some indicating sound. The humming sound indicates the transformer is working.
Does the unit have photoeye? Cover photoeye with black tape.
Test outlet with circuit analyzer.
Check outlet voltage: if you have 120Volt then output is 10% or 12Volts. If you have reduced voltage, then output is still 10% but might be lower than needed to operate bulbs.
Plug timer into different outlet.
Test output terminals with low voltage tester.
Did you have power outage or nearby lightning strike? Transformers are not protected from surge.
Suggest you contact kitchler.
Kitchler.com website is useless
888-412-4877
7711 E Pleasant Valley Rd
PO Box 318010
Cleveland, OH 44131
Kitchler products are probably warranted through the seller.
Kitchler product manuals are almost non-existent.
Scan your product operating manual and parts list into .pdf format and post on web for others to access.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Circuit analyzer does not show all possible problems, and tester might be defective.
Use analyzer on other outlets.
Buy another circuit analyzer.
Buy a multimeter at local hardware, and test for voltage, and continuity, and compare with known outlet that are functioning correctly.
For example outlet may be 240Volt instead of 120V.
Copy following links to see typical circuit analyzer and code:
http://waterheatertimer.org/images/Typical-circuit-analyzer-15.jpg
http://waterheatertimer.org/images/Outlet-polarity-200.jpg

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

HOLD ON!!! The Klein 69127 is an automotive tester to be used for voltages between 6V-24V, AC or DC. The higher voltage in your home could possibly damage the unit as well as yourself. It would be safer for you to use the non contact tester to verify voltage Klien NCVT-1

It only takes a very tiny amount of current to measure voltage. There's always a little tiny current leakage going on, even without contact. Your tester is just telling you the voltage difference between it's own two terminals, even without the other terminal actually touching something, and that difference is 600 volts. Many years ago, my dad showed me a trick using one of those little voltage indicator lights that has little bulb that I think is a neon bulb. If you plug the leads into an outlet, the bulb glows brightly. But if you hold one lead in your hand and stick the other lead into the outlet, the bulb will glow very faintly if the lead is contacting the hot wire. It doesn't glow if you contact the neutral instead. This was very useful to identify hot wires in a box in days before those non-contact voltage detectors that beep.

Need to grab it tight on both sides at black end by pocket clip, and wiggle slightly and pull out at same time. Pocket clip comes off with it.

There are two button cell batteries located in the top of the unit. Try removing the black cap. Some twist off and some pull straight up. Note the polarity of the batteries.