We need more information from the TS.
Is it potted house plants, flowering hanging baskets, a green house garden, cottage garden, or an acre of commercial vegetable plants?

 

https://www.lowes.com/pd/Orbit-1-Outlet-Programmable-Hose-Faucet-Timer/5014592799


Connect that to the hose spigot (top) and the hose to the outlet (bottom). It's programmable. You can set it to run once daily, or on every specific weekday. You can set it to run for 1 minute or up to 99 minutes. It will walk you through the programming process; setup is easy.

Whether you have well water or are hooked up to city water - you only water as much or as little as needed. Of course, if it rains, this unit is not able to cancel watering cycles due to rain or moisture content.

Running a pump means having a reservoir. It also means having a filter to prevent the pump from clogging up. No need to have 120VAC present (assuming the pump is 120VAC powered) or keeping a battery charged up (if the pump is 12VDC).

Since you do this only when you travel this is a good way to keep a garden watered while you're away.

EDIT: Some timers shut the water off suddenly, which can cause Water Hammer, a condition that could burst pipes. I've seen that happen once before. You could put this at the end of the hose just as easily. The only thing that MIGHT burst would be the hose. A long enough hose would easily absorb the shock from water hammer.
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We need more information from the TS.
Is it potted house plants, flowering hanging baskets, a green house garden, cottage garden, or an acre of commercial vegetable plants?

Also what powers the pump? 12VDC ? ? ? 120VAC ? ? ? Solar? Solar might be adaptable for a battery powered controller.

I don't think we need to know how many gallons per minute the pump can deliver, but it might not be bad information to include. If it's drip irrigation and a number of emitters (water outlets) a higher volume would be appropriate.

Two decades ago my wife went in for surgery. She would stay in the hospital for a week then another week at her mom's house. She asked me not to let her garden die. What did I do? I forgot to water them. When I saw them drying up THAT is when I discovered drip irrigation. When my wife came home she was very happy to see a lush garden growing profusely. I got lucky. Lucky in that I didn't kill her garden; that "Lucky". Not the other lucky. Well, maybe I did. I'll never tell.

 

Some timers shut the water off suddenly, which can cause Water Hammer,

I had a blowout like that. It blew the top of the plastic valve spigot connection.

 

There are many water timers available, simple, battery and non-battery operated, mechanical and digital.
Just connect to your tap and feed your drip irrigation system.

 

Now that we know what the project is, there is nothing you can build that will be more reliable, easier to configure, or less total effort than a lamp timer powering the power source for the pump.

The lamp timers I use have little tabs that slide in and out, one tab for each 15 minutes. For you, the total "programming" effort is sliding one tab. That's all. Not sexy, not geeky, no buttons, no LCD displays - and not complicated.

ak

I use a similar timer that switches on a light, as an alarm clock. It works very well.