diff --git a/bindings/pyroot/pythonizations/test/CMakeLists.txt b/bindings/pyroot/pythonizations/test/CMakeLists.txt
index eec078f5546fd..fa8f90b08e5ea 100644
--- a/bindings/pyroot/pythonizations/test/CMakeLists.txt
+++ b/bindings/pyroot/pythonizations/test/CMakeLists.txt
@@ -85,7 +85,8 @@ ROOT_ADD_PYUNITTEST(pyroot_pyz_decorator pythonization_decorator.py)
 
 # Miscellaneous small pythonizations grouped in a single file to avoid paying the
 # Python-startup + import-ROOT overhead once per tiny test: TClass::DynamicCast,
-# TContext context manager, TComplex operators, TIter iteration and TGraph getters.
+# TContext context manager, TComplex operators, TIter iteration, TGraph getters
+# and TParameter arithmetic instantiations.
 ROOT_ADD_PYUNITTEST(pyroot_pyz_misc misc_pyz.py)
 
 # RVec and subclasses pythonizations
diff --git a/bindings/pyroot/pythonizations/test/misc_pyz.py b/bindings/pyroot/pythonizations/test/misc_pyz.py
index d732af025ba59..04fada64fc94c 100644
--- a/bindings/pyroot/pythonizations/test/misc_pyz.py
+++ b/bindings/pyroot/pythonizations/test/misc_pyz.py
@@ -372,5 +372,62 @@ def test_graphmultierrors(self):
         self.assertEqual(list(eyhigh), list(aeyh))
 
 
+class TParameterTemplateInstantiations(unittest.TestCase):
+    """
+    Instantiating TParameter<T> for a type without a dictionary (e.g. char)
+    from the interpreter used to fail with unresolved
+    TParameter<T>::Class() and TParameter<T>::Streamer(TBuffer&) symbols,
+    see https://github.com/root-project/root/issues/10724. Check that all
+    standard arithmetic types can be constructed, printed and serialized
+    from the interpreter.
+    """
+
+    # (type name, value passed to the constructor, value expected from GetVal())
+    # cppyy maps the character types to Python str, so 42 comes back as "*"
+    instantiations = [
+        ("bool", True, True),
+        ("char", 42, "*"),
+        ("signed char", 42, "*"),
+        ("unsigned char", 42, "*"),
+        ("short", 42, 42),
+        ("unsigned short", 42, 42),
+        ("int", 42, 42),
+        ("unsigned int", 42, 42),
+        ("long", 42, 42),
+        ("unsigned long", 42, 42),
+        ("long long", 42, 42),
+        ("unsigned long long", 42, 42),
+        ("float", 0.5, 0.5),
+        ("double", 0.5, 0.5),
+    ]
+
+    def test_construct_and_print(self):
+        for typename, val, expected in self.instantiations:
+            with self.subTest(typename=typename):
+                param = ROOT.TParameter[typename]("p", val)
+                self.assertEqual(param.GetVal(), expected)
+                # Print and ls write to std::cout; exercise the code path
+                # (they used to be uncallable without arguments)
+                param.Print()
+                param.ls()
+
+    def test_has_dictionary(self):
+        for typename, _, _ in self.instantiations:
+            with self.subTest(typename=typename):
+                tclass = ROOT.TClass.GetClass(f"TParameter<{typename}>")
+                self.assertIsNotNone(tclass)
+                self.assertTrue(tclass.HasDictionary())
+
+    def test_io_roundtrip(self):
+        for typename, val, expected in self.instantiations:
+            with self.subTest(typename=typename):
+                param = ROOT.TParameter[typename]("p", val)
+                memfile = ROOT.TMemFile("TParameterTemplateInstantiations.root", "recreate")
+                memfile.WriteObject(param, "p")
+                param_read = memfile.Get("p")
+                self.assertEqual(param_read.GetVal(), expected)
+                memfile.Close()
+
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/core/base/inc/LinkDef3.h b/core/base/inc/LinkDef3.h
index 0ff51977efc32..cc8dc78bd7923 100644
--- a/core/base/inc/LinkDef3.h
+++ b/core/base/inc/LinkDef3.h
@@ -262,10 +262,18 @@
 
 #pragma extra_include "Rtypes.h";
 #pragma link C++ class TParameter<Bool_t>+;
+#pragma link C++ class TParameter<Char_t>+;
+#pragma link C++ class TParameter<signed char>+;
+#pragma link C++ class TParameter<UChar_t>+;
+#pragma link C++ class TParameter<Short_t>+;
+#pragma link C++ class TParameter<UShort_t>+;
 #pragma link C++ class TParameter<Float_t>+;
 #pragma link C++ class TParameter<Double_t>+;
 #pragma link C++ class TParameter<Int_t>+;
+#pragma link C++ class TParameter<UInt_t>+;
 #pragma link C++ class TParameter<Long_t>+;
+#pragma link C++ class TParameter<ULong_t>+;
 #pragma link C++ class TParameter<Long64_t>+;
+#pragma link C++ class TParameter<ULong64_t>+;
 
 #endif
diff --git a/core/base/inc/TParameter.h b/core/base/inc/TParameter.h
index a6a0edfd2dbf9..f52ae32b33d59 100644
--- a/core/base/inc/TParameter.h
+++ b/core/base/inc/TParameter.h
@@ -106,14 +106,14 @@ class TParameter : public TObject {
       return fName.CompareTo(obj->GetName());
    }
 
-   void ls(Option_t *) const override
+   void ls(Option_t * = "") const override
    {
       // Print this parameter content
       TROOT::IndentLevel();
       std::cout << "OBJ: " << IsA()->GetName() << "\t" << fName << " = " << fVal << std::endl;
    }
 
-   void Print(Option_t *) const override
+   void Print(Option_t * = "") const override
    {
       // Print this parameter content
       TROOT::IndentLevel();