The command accepts Unicode arguments.
Very handy. Another way of mapping.

And the last argument can take arbitrary code.
Note that Brill
font contains spacing modifier letters and combining diacritical marks, so kʸʼ can be entered directly.
MWE
\documentclass[12pt]{article}
\usepackage{xcolor}
\usepackage{tikz}
\DeclareTextComposite{\'}{TU}{u}{65}
\DeclareTextCompositeCommand{\'}{TU}{t}{b\textit{l}ub}
\DeclareTextCompositeCommand{\'}{TU}{x}{\textbf{bl\textcolor{red}{u}b}}
\DeclareTextCompositeCommand{\'}{TU}{y}{\textbf{bl\textcolor{red}{i}b}}
\DeclareTextCompositeCommand{\'}{TU}{z}{\fmanat 𔐀𔐳𔑺𔓒}
\DeclareTextCompositeCommand{\'}{TU}{Δ}{\textbf{bl\textcolor{red}{\textit{i}}b}}
\DeclareTextCompositeCommand{\'}{TU}{ѭ}{\textsc{bl\textit{o}b}}
\DeclareTextCompositeCommand{\'}{TU}{अ}{{\fmhiero 𓀀𓋖𓃨\textcolor{red}{𓇨}𓅽}}
\DeclareTextCompositeCommand{\'}{TU}{ꦓ}{\tikz\node[rectangle,draw,fill=yellow!50](b){kʸʼ};}
\DeclareTextComposite{\'}{TU}{v}{30306}
\usepackage{fontspec}
\setmainfont{Brill Roman}
\newfontface\fmcyr{Noto Serif}
\newfontface\fmdev{Noto Sans Devanagari}
\newfontface\fmhiero{Noto Sans Egyptian Hieroglyphs}
\newfontface\fmjav{Noto Sans Javanese}
\newfontface\fmanat{Noto Sans Anatolian Hieroglyphs}
\newfontface\fmzh{Noto Serif SC}
\begin{document}
\begin{tabular}{cccccc}
\verb|\'t| & \verb|\'u| & \verb|\'x| & \verb|\'y| & \verb|\'Δ| & \verb|z| \\
\'t & \'u & \'x & \'y & \'Δ & z \\
& & & & & \\
\verb|\'|{\fmcyr ѭ} & \verb|\'|{\fmdev अ} & \verb|\'|{\fmjav ꦓ} & \tikz\node[circle,draw,fill=green!15,yshift=-1em](a){kʸʼ}; & \verb|\'v| & \verb|\'z| \\
\'ѭ & \'अ & \'ꦓ & kʸʼ & {\fmzh\large \'v} & \'z \\
\end{tabular}
\end{document}
Not an answer, of course; just a kitten playing with string.
Fortunately, the question was asked. And answered. Much appreciated to both.
\v{t}
? – egreg Jun 5 '20 at 13:35\v
behaves differently fort
andp
,c
,k
(it adds a hacek for the latter). – Daniel Harbour Jun 5 '20 at 14:00\v{t}
, I still need other accents to do other work. But let me know if there's something to\v
that I'm missing.) – Daniel Harbour Jun 5 '20 at 14:01