Yes. I know all about this from my hill-walking days. But you need more than one “valid excuse” for unfortunately having to stop just as you were really enjoying that sharp incline. Here are a few more for you (of course, I could never “mend my bike” when hill walking, but anyhow):

- admire the view
- photograph the view
- draw the view
- drink water
- pour water over head
- take or make a phone call on mobile
- write something in log book
- study a plant at close quarters
- draw the plant
- press the plant (provided not rare, in which case, why the interest…??.. err…)
- check map
- mark map
- have a sandwich
- re-fasten boots
- meditate
- apply suncream
- point at piece of ground in nearest field as if to say “could that be the location of an ancient Roman fort?”
- check underside of boots for doggy doo-doos (not if riding a bike though)
- blow nose
- take pretend antibiotic
- check rucksack for something that you suddenly think you might have forgotten
- apply tubular sports bandage thing to knee
- apply lip salve
- set up a tripod with something on top of it and point it towards nearest summit in a map-making/ surveying sort of a way (need to buy and carry said tripod. This one is not the best of my ideas)
- pretend to or actually get cramp
- do “neck exercises” (head forwards and back, side to side) – this looks very good. It smacks of “this hill’s not rigorous enough for me. I need a little additional exercise en route”.

May your love of cycling hither and thither never wither or dither