diff --git a/jax/_src/lax/lax.py b/jax/_src/lax/lax.py
index 4a2887045fb1..4d244f927f30 100644
--- a/jax/_src/lax/lax.py
+++ b/jax/_src/lax/lax.py
@@ -2658,6 +2658,12 @@ def _minmax_translation_rule(c, x, y, *, minmax=None, cmp=None):
 ad.defjvp_zero(lt_p)
 
 
+def _convert_element_type_impl(operand, *, new_dtype, weak_type):
+  if dtypes.is_python_scalar(operand):
+    operand = np.asarray(operand, dtype=new_dtype)
+  return xla.apply_primitive(convert_element_type_p, operand,
+                             new_dtype=new_dtype, weak_type=weak_type)
+
 def _convert_element_type_shape_rule(operand, *, new_dtype, weak_type):
   return operand.shape
 
@@ -2693,7 +2699,7 @@ def _convert_element_type_jvp_rule(tangent, operand , *, new_dtype, weak_type):
     return convert_element_type_p.bind(tangent, new_dtype=new_dtype, weak_type=weak_type)
 
 convert_element_type_p = core.convert_element_type_p
-convert_element_type_p.def_impl(partial(xla.apply_primitive, convert_element_type_p))
+convert_element_type_p.def_impl(_convert_element_type_impl)
 convert_element_type_p.def_abstract_eval(
     partial(standard_abstract_eval, convert_element_type_p,
             _convert_element_type_shape_rule, _convert_element_type_dtype_rule,
diff --git a/jax/experimental/host_callback.py b/jax/experimental/host_callback.py
index a84a23b0407f..961ad1cadd1b 100644
--- a/jax/experimental/host_callback.py
+++ b/jax/experimental/host_callback.py
@@ -934,6 +934,7 @@ def _outside_call_jvp_rule(primals, tangents, **params):
   if not params["identity"]:
     raise NotImplementedError("JVP rule is implemented only for id_tap, not for call.")
   tangent_instantiated = tuple(map(_instantiate_zeros, primals, tangents))
+  tangent_instantiated = tuple(map(ad.replace_float0s, primals, tangent_instantiated))
 
   arg_treedef = params["arg_treedef"]
   # The argument to the jvp tap is a pair of the tapped primals and tangents
@@ -946,6 +947,7 @@ def _outside_call_jvp_rule(primals, tangents, **params):
              arg_treedef=jvp_arg_treedef,
              ))
   out_primals_tapped, out_tangents_tapped = util.split_list(out_all, [len(primals)])
+  out_tangents_tapped = map(ad.recast_to_float0, out_primals_tapped, out_tangents_tapped)
   return tuple(out_primals_tapped), tuple(out_tangents_tapped)
 
 
diff --git a/tests/host_callback_test.py b/tests/host_callback_test.py
index a0d74caca76f..87934ccff2f6 100644
--- a/tests/host_callback_test.py
+++ b/tests/host_callback_test.py
@@ -1028,7 +1028,7 @@ def func(x, yint):
           2 )
         transforms: ['jvp', 'transpose'] what: pair
         ( 2.00
-          False )""", testing_stream.output)
+          0 )""", testing_stream.output)
     testing_stream.reset()
 
   def test_tap_vmap(self):
@@ -1590,8 +1590,8 @@ def padded_sum(x):
               ( 3 ) ) )
           ( ( [0.  0.1 0.2 0.3 0.4]
               [0.  0.2 0.4 0.6 0.8] )
-            ( ( False )
-              ( False ) ) ) )""", testing_stream.output)
+            ( ( 0 )
+              ( 0 ) ) ) )""", testing_stream.output)
     testing_stream.reset()
 
     # Now with JIT
diff --git a/tests/random_test.py b/tests/random_test.py
index 41fa226bc71a..3eb3e6b54bf5 100644
--- a/tests/random_test.py
+++ b/tests/random_test.py
@@ -746,6 +746,8 @@ def f(x):
     grad(lambda x: jnp.sum(vmap(f)(x)))(jnp.ones(2))
 
   def testNoOpByOpUnderHash(self):
+    if not config.omnistaging_enabled:
+      raise SkipTest("test requires omnistaging")
     def fail(*args, **kwargs): assert False
     apply_primitive, xla.apply_primitive = xla.apply_primitive, fail
     try: