I have installed a Utilitech timer switch #0141224 on one of three switches. The switches are all in a row but I only want the last (rightmost) switch changed out. Do I need a jumper from switch 2 to 3? The program isn't working, despite wiring, rewiring, rechecking and reprogramming. Please help!

Troubleshoot walk-thru on following link:
http://waterheatertimer.org/How-to-troubleshoot-timers.html#in-wall

This timer is sold under various different brands, manuals appear following link:
http://waterheatertimer.org/Programmable.html#0141224

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

Modern timer batteries are built into the circuit board and not replaceable ... sounds like a different problem since battery is back up carryover for power outage.
Push override and see if load operates.
Troubleshoot resources and manual:
http://waterheatertimer.org/How-to-troubleshoot-timers.html
http://waterheatertimer.org/Programmable.html#0141224

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

Check wiring for single-pole timers:
http://waterheatertimer.org/How-to-wire-timers.html

Gene

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

Copy following link for TM029 aka LW60418/ 0141224:
http://waterheatertimer.org/Program-wire-Utilitec-0141224.html

Add a comment and describe timer in detail.

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

Sounds like this was probably a three-way switch you are replacing as there is no neutral (white) wire in the box. If so, you can splice the white wire to the green wire in other three-way switch box; then hook the green wire in the box you are placing the timer to the white wire of the Utilitech timer.

1) Utilitec timers cannot be used for multiple switch replacement.
They replace only single-pole switch.

2) Open following link to see specific timers that can be used for 3-way.
http://waterheatertimer.org/GE-timers-and-manuals.html#15071

3) In your case you have 3 different switches that control outside lights: so you have two 3-way switches and one 4-way switch.
Open following link to see typical 4-way wiring.
http://waterheatertimer.org/images/Typical-3-Way-switches-450.jpg

4) 3-way timer will replace one of the 3-way, but not the 4-way.
The timer can be used in place of the 4-way switch.
Identify 4-way because it has 4 screws and 4 wires (excluding ground wire)

5) Keep in mind that 3-way timers replace one of the 3-way switches.
But wiring has to be changed at the remaining 3-way switch.
Open following link to read why wiring is changed at remaining 3-way:
http://waterheatertimer.org/ST01C-program.html#3way
Wiring at the 4-way switch is left the same.
When you buy the timer, read manual carefully for correct wiring, or add a comment to this thread, and I will help more.

Add a comment for more free help.
Also take advantage of fixya expert assistance live.
For a price, expert works with you while you work on timer or any do-it-yourself project.
Fixya is always less expensive than a service call.

Try following page:
Page has links to Utilitec manuals and programming steps.
http://waterheatertimer.org/Program-wire-Utilitec-0141224.html

Also add a comment and say exactly which buttons are on the timer, or what timer looks like, and I can probably identify timer and provide instructions.

Utilitec LW60418 is same as 0141224

See How to install and program Utilitec LW60418

Utilitec timer: manuals and instructions for in-wall programmable

Utilitec LW60418 - Lowes 0141224

Utilitec LW60419 - Lowes 0192773

I believe it is a single pole only, and also requires a neutral to operate.I'm assuming it has black(line) red(load) white(neutral) green(ground) If you need a three-way or only have a switch leg in your box (no white wires) then I'd recommend one of intematic models that can be connected either as a single pole or 3way and requires no neutral.