My incomplete understanding is that the width of pulsars generally seems to depend on their periods and the angle between their magnetic axes and rotational axes. The general trend is for shorter period pulsars to have pulse widths that are a larger fraction of their periods. See On the pulse-width statistics in radio pulsars for some more detail. It looks like there are pulse half widths as narrow as a few degrees (~1/100 of a period), and some that are as wide as ninety degrees (1/4 of a period, meaning that if we were able to see both pulsing sides, the pulsar is on ~1/2 the time).
Given that level of variation, I'm not sure if there is a very general sort of plot of intensity versus phase. Some are nicely Gaussian pulses, with a nice interpulse at 180 degree phase separation, whereas others have much more structure. Take a look at some of the figure in Multi-frequency integrated profiles of pulsars (there are a total of 34 pulsar profiles plotted, and it should be available to all as it was posted to arXiv).