BDAG defines ἐκθαμβέω like this:
ἐκθαμβέω (s. ἔκθαμβος; Orph., Arg. 1217 [tmesis]; PGrenf I 53, 18=Mitt-Wilck. I/2, 131, 18 [IV A.D.]; TestAbr B 13 p. 118, 11 [Stone p. 84]) fut. 3 sg. ἐκθαμβήσει Sir 30:9; 1 aor. pass. ἐξεθαμβήθην, in our lit. only in Mk and only pass. in active sense: to be moved to a relatively intense emotional state because of someth. causing great surprise or perplexity, be very excited Mk 9:15 (the presence of Jesus suggests possible resolution of a dispute; but consideration of Mark’s larger narrative structure leads some scholars to prefer the sense be amazed [as in Galen: CMG V 9, 2 p. 5, 12=XVI 493 K.], which lacks immediate motivation in the scene at hand); be overwhelmed, be alarmed 16:5f; be distressed w. ἀδημονεῖν 14:33.—Cp. θαμβέω in 1:27; 10:32.—DELG s.v. θάμβος. M-M. TW.
Arndt, W., Danker, F. W., & Bauer, W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 303). Chicago: University of Chicago Press.
And ἀδημονέω like this:
ἀδημονέω (Hippocr. et al.; Pla., X.; TestAbr A 7, p. 84, 9 [Stone p. 16]; Jos., Ant 15, 211; 388; POxy 298, 45 [I A.D.] λίαν ἀδημονοῦμεν χάριν τῆς θρεπτῆς Σαραποῦτος; Job 18:20 Aq.; Sym. Ps 60:3 al.) be in anxiety, be distressed, troubled w. λυπεῖσθαι Mt 26:37; w. ἐκθαμβεῖσθαι Mk 14:33; foll. by διότι because Phil 2:26.—MHarl, La Bible et les Pères, ’71, 257.—DELG. M-M.
Arndt, W., Danker, F. W., & Bauer, W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 19). Chicago: University of Chicago Press.
These words seem to describe Jesus' emotional state? If so, can we determine his emotional state with any precision from these words?
ἐκθαμβέω seems to suggest that Jesus was "shocked" while ἀδημονέω seems to suggest "perplexed". Was Jesus somehow taken by surprise by his imminent death? Or was he simply overcome with dread of the imminent ordeal? Was he questioning his strength to endure?