Ticking coming from rebuilt engine.

It may have a mis-adjusted valve. But it would have a pretty bad amount of lash to do so. The lash may be wrong because the push rods were not kept in order when the engine was rebuilt or they did not at least measure them when they put it back together to make sure the distance from lifter to the rocker arm was correct. The other possibility is that the lifters were not replaced or installed wrong and one of them is crushed. This can also be casued if there is a clog in the oil port on the lifter and it will not have the correct valve lash.
The place to start is to ask about the lifters and the psuh rods and have the valve lash measured.

GUESSING TAPPETS AND PUSH-RODS ARE ALL NEW.

I HAVE REMOVED THE VALVE COVER ON ONE OF MY PREVIOUS JEEPS YEARS AGO, AND PUSHED ON ROCKERS AS THE ENGINE RAN, UNTIL I FOUND THE "TAPPER"

I KNOW LITTLE ABOUT HOW YOURS IS SET UP, THE ONLY ADJUSTMENT FOR MINE ARE THE TAPPETS THEMSELVES, AS THEY TAKE UP SLACK, AS WEAR OCCURS.

MY ENGINE HAD QUITE A FEW MILES ON IT, AND MARVEL MYSTERY OIL HAD NOT HELPED THIS TIME.

IT WAS SUGGESTED THAT I REMOVE THE PUSH-ROD FOR THE VALVE/ ROCKER THAT WAS TAPPING----OBTAIN THE "NEXT LONGER" PUSH-ROD (IN MY CASE, IT SEEMS LIKE THAT WAS LESS THAN .010" LONGER [TEN THOUSANDTHS] I JUST DO NOT REMEMBER, COULD HAVE BEEN 5-7)

REGARDLESS, IT WAS NOT ENOUGH TO "BOTTOM OUT" AND BEND THE PUSH-ROD [EVEN SLIGHTLY] AS IT TRAVELED UP

WHAT THIS DID DO WAS TO RE-POSITION THE THE "DEPTH OF THE PLUNGER" INSIDE THE TAPPET---FOR INSTANCE .010" DEEPER THAN IT PREVIOUSLY WAS...AND IT BEGAN SEALING AS IT SHOULD

IN CASE YOU REALLY DON'T UNDERSTAND SORTA HOW THEY WORK...I'LL GIVE YOU THE COUNTRY-BOY VERSION

A BRAND NEW TAPPET IS SPRINGY--MAYBE (GUESS) 150 THOUSANDTHS OF FREE TRAVEL....WHEN YOU INSTALL THE NEW PUSH-RODS, YOU SORTA PRE-LOAD THEM...LETS SAY PUSH OUT 100 THOUSANDTHS--LEAVING 50 THOUSANDTHS OF SPRING IN THE TAPPET....THIS IS SORTA DONE BY SELECTING A ROD THAT WILL DO THIS.

AT MINIMUM, YOU GET 1 TAPPET AS LOW AS IT WILL GO ON THE CAM---INSERT A "TEST" PUSH-ROD. INSURE THERE IS NO SLOP IN THE SYSTEM, AND USING A DIAL INDICATOR, PUSH DOWN ON THE ON THE PUSH-ROD SIDE UNTIL YOU BOTTOM OUT THE PLUNGER INSIDE THE TAPPET....IN THIS CASE, YOU WOULD MEASURE/SELECT, AND TRY A PUSH-ROD THAT LEAVES US 50 THOUSANDTHS OF SPRING (FROM "REST" TO "BOTTOMED OUT") I CHECK ALL 12 VALVES ON MY JEEP, ALL OF THE PUSH-RODS NORMALLY WIND UP A GIVING ME THE DESIRED 50 THOUSANDTH OF OF SPRING. (MY 12 PUSH-RODS ARE IDENTICAL)

NOW, WHAT WE HAVE IS 100 THOUSANDTHS OF UPWARD SPRING THAT WILL MAKE UP FOR WEAR AS ALL OF THE PARTS WEAR IN THE FUTURE....FOR INSTANCE IN 500 MILES THE 100 MAY BE 99...12,000 MILES IT MAY BE 97 AND SO ON.

THIS IS EVERY THING THAT IS WEARING--CAM LOBE--BOTTOM OF TAPPET---TOP OF TAPPET--LOW END OF PUSH-ROD---UPPER END OF PUSH-ROD---BOTH TIPS OF THE ROCKER ARM--ALSO THE ROCKER ARM PIVOT, AND WHAT IT PIVOTS ON, AND LAST THE TIP OF THE VALVE STEM..........THE ONLY THING THAT SORTA REVERSES THIS WEAR, IS THE LITTLE BIT THAT THE VALVE S.UCKS INTO THE SEAT, AS IT WEARS IN (ACTUALLY MAKING THE VALVE STEM LONGER PER SAY)

REMEMBER EVERY THING WAS NEW!

NOW, ONCE OIL PRESSURE IS INJECTED INTO THE TAPPET, THE SPRINGY IS GONE--THIS PUPPY LOCKS UP LIKE A HYDRAULIC JACK! NO MORE PUSHING THE SPRINGY-NESS WITH YOU FINGER......AS IS RISES DUE TO CAM LOBE ACTION, THE VALVE GETS PUSHED OPEN (THERE IS NO SLACK AS IT PUSHES)

WHEN THE ENGINE IS RUNNING AND THERE IS "OIL PRESSURE" THE LOBE LOWERS THE ROCKER AND THE VALVE CLOSES........IF YOU DON'T TAKE NOTHING ELSE IN, THIS IS THE PART YOU NEED TO REMEMBER THE MOST!

WHEN THE TAPPET DROPS DOWN--IT IS NOW DROPPED INTO "OIL PRESSURE", IN AN OIL GALLEY, THE OIL PRESSURE SORTA "UNLOCKS" THE TAPPET (LIKE RELEASING A HYDRAULIC JACK) RATHER THE PLUNGER PART OF IT, EXCEPT "OUR HYDRAULIC JACK CYLINDER" IS SPRING LOADED!!! IT PUSHES THE SLACK OUT, BY PUSHING THE PUSH-ROD UPWARD. THIS MIGHT BE MILLIONTHS OF AN INCH, BUT IT RE-ADJUSTS EVERY TIME IT GOES DOWN.....OVER TIME, THE TAPPET'S PLUNGER RISES MORE AND MORE, SLACK IS MINIMIZED.

WITH "TAPPETS",YOU DO NOT HAVE TO GO IN, AS WITH OLD VEHICLES AND ADJUST THE "LIFTERS" BY EITHER ADJUSTING THE LIFTER LONGER (AS IN MY 1946 WILLYS JEEP FLATHEAD ENGINE) OR ON SOME CARS, A SET SCREW TYPE ADJUSTMENT ON THE ROCKER ARM TO TAKE OUT SLACK

SO IN THE END HERE---OR THE MORAL OF THIS WHOLE STORY

YOU WILL NOT BE ABLE TO "SELECT A PUSH-ROD" WITH AN "OIL FILLED" TAPPET....SO DON'T TRY!

IF YOU TRY "MY METHOD" BY INSTALLING ONE PUSH-ROD, ON THE "PROBLEM CHILD TAPPER"

ALWAYS INCREASE BY A FEW THOUSANDTHS---DON'T MAKE A BIG INCREASEIF THIS IS A USED ENGINE, OR USED TAPPETS....YOUR SLIGHT INCREASE MIGHT JUST BE "MAKING UP" FOR SLACK THAT HAS ALREADY BEEN TAKEN OUTTOO MUCH, AND YOU BOTTOM OUT THE PLUNGER IN THE TAPPET

DO NOT GO SHORTER---YOU MAY BE CHEATING YOURSELF OUT OF "SELF ADJUSTMENT"

NOW HERE'S THE KICKER, I'VE HEARD PEOPLE SAY,---"IF I PUT A LONGER PUSH-ROD IN, IT WILL BE TOO LONG!"......YES THIS IS CORRECT, TO AN EXTENT! THE VALVE MAY SLIGHTLY STAY CRACKED OPEN FOR SECONDS!....AS SOON AS OIL PRESSURE HITS THE LOWERED TAPPET---IT WILL ADJUST THE TAPPET PLUNGER, "DOWN", BY A FEW THOUSANDTHS---AT THE SAME TIME THE VALVE WILL SEAT CORRECTLY, AND THE PUSH-ROD WILL PUSH ON THE PLUNGER PART OF THE TAPPET AND EVERYBODY IN THE SYSTEM WILL GO BACK TO "ZERO PLAY"

THIS IS THE REASON TO PUT THE SLIGHTLY LONGER PUSH-ROD IN---TO MAKE THE TAPPETS PLUNGER MOVE SLIGHTLY (RATHER, RE-LOCATE A LITTLE DEEPER), IN HOPES THAT IT MIGHT START "SEALING OFF" CORRECTLY BEFORE IT PUSHES THE PUSH-ROD, OR WHEN IT RE-ADJUSTS.

A TAPPET IS A COMPLICATED LITTLE BOOGER! SEE THIS LINK!

https://www.2carpros.com/questions/jeep-wrangler-2002-jeep-wrangler-removing-lifters

THE MEDIC