If it is emitting its value by light, as you move away or closer to it, it's value will shift up/down (red/blue shift), and it's rate of 'ticking' will change up/down. You can't prove that something far away happened in the past or the future using your construction.
It's value won't shift down. Yes, you don't measure it with a wristwatch, but you measure it with a device that receives the value on the clock, and display it.
Just like any other physical measures. You don't measure nearly any of them with a wristwatch (only proper time/aging) but with a device that is constructed according to the definition of that physical measure.
If you are sending pulses, the pulses will get further apart as you accelerate away and shorter as you slow down. This will cause your clocks to desynchronize and you’ll find that a different amount of time has passed for you than your own clock. This is called relativity. You can say that your flashing clock is The One True Clock and if everything in the universe agrees with you, then I suppose it’s true. But one persons clock won’t be flashing at the same speed as another ones. This includes earth where one season we will be moving away (slower) and another we will be getting closer (speeding up). That’s be pretty annoying.
