Identified by @ssastry while debugging T213922:

In T213922#4886102, @ssastry wrote:

So I patched html2wt with as follows (since this is triggered only on edited HTML and I wanted to test it with regular HTML),

diff --git a/lib/html2wt/WikitextSerializer.js b/lib/html2wt/WikitextSerializer.js
index d052a47e0..9470070fa 100644
--- a/lib/html2wt/WikitextSerializer.js
+++ b/lib/html2wt/WikitextSerializer.js
@@ -782,11 +782,12 @@ WikitextSerializer.prototype.serializeFromParts = Promise.async(function *(state
                var fetched = false;
                try {
                        var apiResp = null;
-                       if (isTpl && useTplData) {
+                       if (isTpl && true) {
                                var href = tplHref.replace(/^\.\//, '');
                                apiResp = yield TemplateDataRequest.promise(env, href, Util.makeHash(["templatedata", href]));
                        }
                        tplData = apiResp && apiResp[Object.keys(apiResp)[0]];
+                       console.log("TPLDATA: " + JSON.stringify(tplData));

Now, when I rut it with the HTML of fawiki's infobox, see the output:

[subbu@earth:~/work/wmf/parsoid] parse.js --html2wt --prefix fawiki  --trace apirequest< /tmp/fa.html 
....
[ApiRequest]   | #3 Starting HTTP request:  {"method":"GET","qs":{"format":"json","action":"templatedata","includeMissingTitles":"1","titles":"الگو:Infobox_Officeholder"},"followRedirect":true,"uri":"https://fa.wikipedia.org/w/api.php","timeout":30000,"headers":{"X-Request-ID":null,"User-Agent":"Parsoid/0.10.0+git","Connection":"close"},"strictSSL":true}
....
TPLDATA: {"title":"الگو:Infobox Officeholder","notemplatedata":"","params":[]}

In T213922#4886149, @matmarex wrote:

@ssastry Note that the Parsoid query is for "Infobox Officeholder" (with uppercase "O"), which is a redirect to "Infobox officeholder" (lowercase "o"). Only the latter page has templatedata. Parsoid should probably ask the MediaWiki API to follow redirects (&redirects=1). But that seems like a separate issue.

In T213922#4886360, @ssastry wrote:

In my snippet I pasted above with the API trace, see that we already have "followRedirect":true. Is that the wrong param?

In T213922#4886754, @matmarex wrote:

I'm not familiar with that library, but it looks like this is the library's parameter for following HTTP redirects, rather than a query parameter for following MediaWiki redirects.