for showing thinking (has nothing to do with ponder)
usually uci programs (and xboard too) output thinking while calculating.
In uci this is done with info lines (depth-score-nodes-time at least).
I noticed that AXW outputs one info line finally per move BUT after the sent bestmove,
which is probably the reason it is not recorded into the game file by the GUI.
example from Stockfish 11
(not all fields are mandatory ofc, like tbhits, nps, multipv etc...)
Split from #2:
AXW 0.07