How to add Korean as the 2nd IME to elemetaryOS Juno with Japanese IME?

I want to add a Korean input method on an elementary OS Juno system which currently running fcitx-mozc with a US-101 keyboard. Because of some business restrictions, I cannot freely sacrifice Mozc only for a Korean IME or switch from fcitx to iBus. The current steps I have done is the following: I installed fcitx-hangul through APT command. I opened fcitx-config-gtk3 menu, added a Keyboard-Korean option from the list, and did logout/in. It still toggles EnglishJapanese fine. But, no signs for Korean input options show up. Is there any way I can switch those 3 languages on fcitx with minimal environmental changes or additions? I am aiming at a goal that can enable Japanese IME by hitting left-CTRL + SPACE, and enable Korean IME by right-CTRL + SPACE (or some other short-cut key). Any suggestions. Or, what process am I missing? Thanks :)