How do you visualize the frequency spectrum for a digital waveform?
I believe you are referring to analog waveforms, just a rectangular one, or stream of pulses that are coninuous with time (analog)- unless you meant specifically a sampled square wave (which I would call a digital waveform). 

In any event, the single rectangular pulse, and the repeated one are both a Sinc function in frequency! It is just when you repeat a waveform in time, it can only exist in frequency at multiples of the repetition rate. In the case of a single rectangular waveform, the Fourier Transform as you stated is a Sinc function, with the first null at 1/T where T is the width of the pulse.  If you repeat that pulse in time, then the resulting frequency spectrum can only exist at that repetition rate and all higher harmonics, so you get samples (in frequency) of the same Sinc function!

The easiest way to understand why this occurs (that the frequency can only exist in individual tones) is to review the Fourier Series Expansion where you will see that the resulting pattern can not repeat in time unless each sinusoidal component is also repeating exactly within the 0 to T interval used for the expansion.

I will explain with some graphics:

First consider the Fourier Transforms below for an impulse, a rectangular pulse, and a constant level in time, and their associated transforms in Frequency. These are the results in the frequency domain for a single event of these waveforms in time. 
 

Now consider a repeating stream of impulses in time. Notice we can derive the frequency domain result by first drawing the base function from above, and then knowing in this case since it is repeating every 2 seconds (1/2 Hz rate), it can only exist in Frequency at 0 (DC), and integer harmonics of 1/2 Hz as shown. So impulses in time result in impulses in frequency!



Now for your example specifically. We do the same thing: We first draw the Fourier Transform of the base pulse which has a width of 0.05 seconds in this case, resulting in the first null of the Sinc function to be at 1/0.05 = 20 Hz. We then note that this waveform is repeating at a 10 Hz rate, so it can only exist at DC, 10 Hz and all higher harmonics in frequency. Interestingly in this case, all the even harmonics are nulls of the Sinc function, so for this case specifically, with a 50% duty cycle the frequency components are the 1st, 3rd, 5th, etc harmonics, but importantly samples of the same Sinc function!



Now consider a 25% duty cycle square wave. I show the 3 down-arrows and one up arrow as a take-away that the division in time of 4 results in the 4 harmonic to be in the null (a 10% duty cycle would have the 10th harmonic in the null). This is doing the same thing as before, we first draw the frequency envelope as a Sinc function, and then if the waveform is repeating we show the frequency locations as only existing at multiples of the repetition rate.



Now finally, for random bit streams we would get a continuous spectrum; if the bit stream is a stream of rectangular pulses, the result would be a continuous Sinc function in frequency given by the minimum pulse width. In this case, if truly random, there is no repetition pattern and therefore no individual frequency components, only a distribution. One way to visualize this is the resulting pattern can be decomposed into individual single rectangular pulses; each one creating the Sinc function in frequency. There phase relationship depends on when they each occur in time, and since that is random there will not be a consistent cancellation or addition to create any other pattern in frequency and a continuous spectrum is maintained (as such occurs when the repeat at a consistent rate).