Do you vary your bids or pause your campaign at certain times based on this?
Absolutely. Altering bids based on time of day (typically) requires the assistance of technology, but altering your strategy based on day of week is quite a bit more manageable can generate significant lifts in revenue and ROI.
It is strange like you mentioned, clicks don't decrease as much as conversion rates do.
For smaller businesses, breaking conversions down to this granularity can be revealing. If you break a week down into 168 hour parts, but see relatively few conversions, you may only see 5 conversions in a one hour period(say between 7pm and 8pm) on Tuesday nights. Whereas the same hour on Friday will see 2. If you collect this data over an 8 week period, you'll begin to see that the Tuesday hour has 40 conversions (8 x 5) vs 16 (8 x 2)on Friday for example. So the Tuesday hour has 2.5 more conversions(40 / 16), but not nearly 2.5 times the traffic levels.
Its my experience that you may see 1,000 clicks in the Tuesday hour but 800 or so on the Friday night hour. If daily caps are in effect, than you may very well see 1,000 clicks in both hours. But, the difference between a 4% conversion rate and a 1.6% conversion rate is obviouly large. If your avg, cpc is $1, than shifting the $1K budget from the friday hour back to the Tuesday hour, could very well yield double, 40 more conversions in the Tuesday hour, or 24 more total on your week.
If the Tuesday 7pm to 8pm hour happens to be your most heavy-hitting hour, driving 20% or so of all of your conversions, a move like this can can make a noticeable difference to your overall conversion, allowing you to afford higher CPC's.