Gstreamer: vaapih264enc missing, even though other vaapi elements are present

Question

I'm trying to use VAAPI with Gstreamer on Ubuntu 18.04 to encode H.264. I'm pretty sure I have all necessary packages installed (gstreamer1.0-vaapi, vainfo, i965-va-driver and all dependencies).

VAAPI is enabled and works:

 $ vainfo
libva info: VA-API version 1.1.0
libva info: va_getDriverName() returns 0
libva info: Trying to open /usr/lib/x86_64-linux-gnu/dri/i965_drv_video.so
libva info: Found init function __vaDriverInit_1_1
libva info: va_openDriver() returns 0
vainfo: VA-API version: 1.1 (libva 2.1.0)
vainfo: Driver version: Intel i965 driver for Intel(R) Haswell Mobile - 2.1.0
vainfo: Supported profile and entrypoints
      VAProfileMPEG2Simple            : VAEntrypointVLD
      VAProfileMPEG2Simple            : VAEntrypointEncSlice
      VAProfileMPEG2Main              : VAEntrypointVLD
      VAProfileMPEG2Main              : VAEntrypointEncSlice
      VAProfileH264ConstrainedBaseline: VAEntrypointVLD
      VAProfileH264ConstrainedBaseline: VAEntrypointEncSlice
      VAProfileH264Main               : VAEntrypointVLD
      VAProfileH264Main               : VAEntrypointEncSlice
      VAProfileH264High               : VAEntrypointVLD
      VAProfileH264High               : VAEntrypointEncSlice
      VAProfileH264MultiviewHigh      : VAEntrypointVLD
      VAProfileH264MultiviewHigh      : VAEntrypointEncSlice
      VAProfileH264StereoHigh         : VAEntrypointVLD
      VAProfileH264StereoHigh         : VAEntrypointEncSlice
      VAProfileVC1Simple              : VAEntrypointVLD
      VAProfileVC1Main                : VAEntrypointVLD
      VAProfileVC1Advanced            : VAEntrypointVLD
      VAProfileNone                   : VAEntrypointVideoProc
      VAProfileJPEGBaseline           : VAEntrypointVLD

So VAAPI is there and supports H.264. Gstreamer also has VAAPI support:

$ gst-inspect-1.0 vaapi
Plugin Details:
  Name                     vaapi
  Description              VA-API based elements
  Filename                 /usr/lib/x86_64-linux-gnu/gstreamer-1.0/libgstvaapi.so
  Version                  1.14.5
  License                  LGPL
  Source module            gstreamer-vaapi
  Source release date      2019-05-29
  Binary package           gstreamer-vaapi
  Origin URL               http://bugzilla.gnome.org/enter_bug.cgi?product=GStreamer

  vaapisink: VA-API sink
  vaapidecodebin: VA-API Decode Bin
  vaapipostproc: VA-API video postprocessing
  vaapimpeg2dec: VA-API MPEG2 decoder

  4 features:
  +-- 4 elements

However, what's conspicuously absent is vaapih264enc. AFAICT it's even compiled into the package:

$ strings /usr/lib/x86_64-linux-gnu/gstreamer-1.0/libgstvaapi.so | grep h264
gst_h264_nal_parser_free
gst_h264_parser_parse_sps
[...]
vaapih264feienc
vaapih264enc
video/x-h264
[...]

So what do I have to do to actually enable the corresponding Gstreamer element?