Thanks to the suggestion by
rfosness88, I eventually found a program called PS Remote:
PSRemote - Software Features Canon PowerShot Remote Control Program
which allows me to do exactly what I want.
Unfortunately, after researching the program, I found that
it does not work with certain PowerShot cameras, including mine (Canon A650 IS).
I may look for a used A70 or something else that is on the list of cameras that work with the program. Here's the list:
Pro series
Pro90IS, Pro1
G-series
G1, G2, G3, G5, G6, G7, G9, G10
S-series
S30, S40, S45, S50, S60, S70, S80, S1 IS, S2 IS, S3 IS, S5 IS, SX100 IS, SX110 IS
A-series
A30, A40, A60, A70, A75, A80, A85, A95, A300, A310, A400, A510, A520, A620, A640
Digital IXUS
SD100 (Digital IXUS II), SD110 (Digital IXUS IIs), S230 (Digital IXUS 330), S400 (Digital IXUS 400), S410 (Digital IXUS 430), S500 (Digital IXUS 500)
I may also look for some other camera that just supports automated long-term timed shutter operation. The A650 does,
but only allows a maximum of 10 pictures timed a maximum of 30 seconds apart.
If only they had these maximums raised to 60 seconds between pictures, and unlimited number of pictures (limited only by memory) then it would do exactly what I need it to.
If anyone knows of a camera model that does this, please feel free to let me know. I may be in the market.
Thanks.