In the attached pic, I need to enter longs when the red signal crosses above the lower band and exit longs when the red signal crosses below the upper band. The TurnUp(Down) and CrossOver() signals are not helping at all here. In fact, using default TurnUp(Down) and CrossOver() actually produce disastrous results.

For entering longs when the signal crosses above the lower threshold, does it look like i-2, -1 and i+1 or i+2 are needed? Same question for the red signal crossing below the upper threshold?

CrossOver and TurnUp is documented in the QuickRef (hit F11 to open up the tool, then start typing in the first letters of a keyword).

To me, "don't work" and "not helping at all here" and "disastrous results" do not work at all. Same with "i-2, -1 and i+1 or i+2" which is cryptic enough to explain what's wrong with your code (where is it?) and how can we help improve it. Could you explain your task more clearly with a Strategy code sample and a symbol to apply it to? What goes contrary to your expectations and on which bar should a signal take place instead?

It worked out that the buys had to be based on signal turnups below the lower band, and sells based on signal turndowns above the upper band.

Whatever works for you is fine by me. Glad that you've resolved it on your own.