A bit of progress has been made.
Apparently the issue is with TinkerTool 3.7.
It seems that it is only when I enable TT (General) "Place scroll arrows together at both ends", that no arrows are displayed in System Preferences/Sound/Sound Effects.
But if I select "Place scroll arrows at both ends", then the scroll arrows in Sound Effects appear normally.
I have repeated this test numerous times, always with the same result.
I have written to the TinkerTool developer (Dr. Marcel Bresink) and asked for his thoughts. When I hear from him, I'll post his comments.
P. S.
Dr. Bresink had this to offer (edited):
I could not reproduce this problem with any Mac OS X 10.4.9 Intel system. However, the exact results may depend on your personal language preferences and the ppi resolution of your screen.
Re: Apple's System Preferences application. I would assume you have a special combination of settings in your personal user defaults that cause System Preferences to behave this way.
You should also verify that you are not running some software that is "patching" Mac OS X to alter its normal user interface.
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The only approximation I have to a user interface patch relates to a few Haxies. So I disabled all of those to verify that Haxies were or were not involved. Even with all Haxies disabled, the scroll bar condition continues as first described.
Seems 'tis a condition I will grow to love, well, at least learn to live with.